GGW-mod2: Factor Analysis

Setup

Data preparation

## Warning in ifelse(as.numeric(as.character(structure(c(48L, 47L, 50L, 43L, :
## NAs introduced by coercion

## Warning in ifelse(as.numeric(as.character(structure(c(48L, 47L, 50L, 43L, :
## NAs introduced by coercion

## Warning in ifelse(as.numeric(as.character(structure(c(48L, 47L, 50L, 43L, :
## NAs introduced by coercion

## Warning in ifelse(as.numeric(as.character(structure(c(44L, 48L, 49L, 45L, :
## NAs introduced by coercion

## Warning in ifelse(as.numeric(as.character(structure(c(44L, 48L, 49L, 45L, :
## NAs introduced by coercion

## Warning in ifelse(as.numeric(as.character(structure(c(44L, 48L, 49L, 45L, :
## NAs introduced by coercion

## Warning in Ops.factor(d_clean_4[, i], 4): '-' not meaningful for factors

Data examination

Study 1 (2015-12-15, 2 conditions, between-subjects)

Demographics

## Warning in mutate_impl(.data, dots): NAs introduced by coercion

Study 1: Exclusion

did_not_finish	failed_catch_trial	did_not_provide_yob	too_young	TOTAL_excluded	TOTAL_participated	OVERALL_TOTAL
14	19	15	0	48	405	453

Study 1: Sample size

condition	n
beetle	200
robot	205
all	405

Study 1: Study duration (minutes)

condition	min_duration	max_duration	median_duration	mean_duration	sd_duration
beetle	0.77	119.12	2.77	3.92	8.50
robot	0.83	15.77	2.58	3.24	2.11
all	0.77	119.12	2.67	3.58	6.16

## Joining by: c("condition", "min_age", "max_age", "median_age", "mean_age", "sd_age")

## Warning: joining character vector and factor, coercing into character
## vector

Study 1: Participant age (years; approximate)

condition	min_age	max_age	median_age	mean_age	sd_age
beetle	19	70	31	34.24	10.64
robot	20	75	32	35.11	11.20
all	19	75	32	34.68	10.92

Study 1: Participant gender

condition	m	f	other
beetle	119	81	0
robot	121	82	2
all	240	163	2

Study 1: Participant race/ethnicity

condition	asian_east	asian_other	asian_south	black	hispanic	middle_eastern	multiracial	native_american	other_prefno	pac_islander	white
beetle	20	0	6	8	9	1	11	1	1	1	142
robot	16	2	2	15	9	1	9	1	1	1	148
all	36	2	8	23	18	2	20	2	2	2	290

Study 1: Participant religion

condition	buddhism	christianity	hinduism	islam	judaism	multireligious	none	other	other_prefno
beetle	3	81	2	2	4	0	101	3	4
robot	2	87	0	0	5	3	100	3	5
all	5	168	2	2	9	3	201	6	9

Exploratory factor analysis

EFA: BEETLE condition

Step 1: Determine how many factors to extract

Step 2: Run EFA without rotation

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Factor Analysis using method =  minres
## Call: fa(r = d1_beetle, nfactors = nfactors_d1_beetle, rotate = "none", 
##     fm = "minres", cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                 MR1   MR2   h2    u2 com
## happy          0.86 -0.10 0.75 0.249 1.0
## depressed      0.86 -0.31 0.84 0.157 1.3
## fear           0.69  0.32 0.58 0.419 1.4
## angry          0.79 -0.04 0.62 0.376 1.0
## calm           0.79  0.20 0.66 0.341 1.1
## sounds         0.38  0.58 0.47 0.525 1.7
## seeing         0.34  0.74 0.66 0.341 1.4
## temperature    0.40  0.70 0.65 0.350 1.6
## odors          0.41  0.57 0.50 0.500 1.8
## depth          0.50  0.40 0.41 0.590 1.9
## computations   0.63 -0.45 0.60 0.404 1.8
## thoughts       0.82 -0.07 0.68 0.320 1.0
## reasoning      0.84 -0.15 0.73 0.266 1.1
## remembering    0.67  0.24 0.51 0.490 1.2
## beliefs        0.76 -0.48 0.81 0.195 1.7
## hungry         0.38  0.78 0.76 0.237 1.5
## tired          0.66  0.41 0.60 0.403 1.7
## pain           0.54  0.61 0.67 0.326 2.0
## nauseated      0.82  0.05 0.68 0.322 1.0
## safe           0.70  0.23 0.54 0.458 1.2
## love           0.87 -0.27 0.82 0.178 1.2
## recognizing    0.76 -0.03 0.58 0.418 1.0
## communicating  0.61  0.20 0.42 0.584 1.2
## guilt          0.81 -0.47 0.88 0.119 1.6
## disrespected   0.81 -0.42 0.83 0.167 1.5
## free_will      0.68  0.17 0.49 0.512 1.1
## choices        0.67  0.36 0.58 0.419 1.5
## self_restraint 0.80 -0.19 0.68 0.323 1.1
## intentions     0.70  0.24 0.55 0.450 1.2
## goal           0.64  0.30 0.50 0.501 1.4
## conscious      0.73  0.16 0.56 0.437 1.1
## self_aware     0.75  0.00 0.56 0.438 1.0
## desires        0.73  0.14 0.56 0.444 1.1
## embarrassed    0.78 -0.55 0.91 0.091 1.8
## emo_recog      0.80 -0.42 0.83 0.174 1.5
## joy            0.88 -0.14 0.79 0.213 1.1
## morality       0.77 -0.38 0.74 0.262 1.5
## personality    0.82 -0.24 0.73 0.265 1.2
## pleasure       0.78  0.21 0.66 0.339 1.1
## pride          0.85 -0.40 0.88 0.120 1.4
## 
##                         MR1  MR2
## SS loadings           20.64 5.64
## Proportion Var         0.52 0.14
## Cumulative Var         0.52 0.66
## Proportion Explained   0.79 0.21
## Cumulative Proportion  0.79 1.00
## 
## Mean item complexity =  1.4
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  69.39 with Chi Square of  12824.86
## The degrees of freedom for the model are 701  and the objective function was  31.95 
## 
## The root mean square of the residuals (RMSR) is  0.04 
## The df corrected root mean square of the residuals is  0.05 
## 
## The harmonic number of observations is  200 with the empirical chi square  612.68  with prob <  0.99 
## The total number of observations was  200  with MLE Chi Square =  5862.79  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.519
## RMSEA index =  0.201  and the 90 % confidence intervals are  0.187 NA
## BIC =  2148.67
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                MR1 MR2
## Correlation of scores with factors               1   1
## Multiple R square of scores with factors         1   1
## Minimum correlation of possible factor scores    1   1

Step 3: Run EFA with oblimin rotation

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Loading required namespace: GPArotation

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate =
## rotate, : A Heywood case was detected. Examine the loadings carefully.

## Factor Analysis using method =  minres
## Call: fa(r = d1_beetle, nfactors = nfactors_d1_beetle, rotate = "oblimin", 
##     fm = "minres", cor = "poly")
## 
##  Warning: A Heywood case was detected. 
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   h2    u2 com
## happy           0.76  0.23 0.75 0.249 1.2
## depressed       0.91  0.02 0.84 0.157 1.0
## fear            0.34  0.58 0.58 0.419 1.6
## angry           0.66  0.27 0.62 0.376 1.3
## calm            0.50  0.50 0.66 0.341 2.0
## sounds         -0.08  0.71 0.47 0.525 1.0
## seeing         -0.22  0.85 0.66 0.341 1.1
## temperature    -0.15  0.84 0.65 0.350 1.1
## odors          -0.05  0.72 0.50 0.500 1.0
## depth           0.14  0.58 0.41 0.590 1.1
## computations    0.81 -0.20 0.60 0.404 1.1
## thoughts        0.71  0.25 0.68 0.320 1.2
## reasoning       0.78  0.18 0.73 0.266 1.1
## remembering     0.39  0.49 0.51 0.490 1.9
## beliefs         0.94 -0.18 0.81 0.195 1.1
## hungry         -0.22  0.92 0.76 0.237 1.1
## tired           0.26  0.65 0.60 0.403 1.3
## pain            0.03  0.81 0.67 0.326 1.0
## nauseated       0.64  0.36 0.68 0.322 1.6
## safe            0.41  0.49 0.54 0.458 1.9
## love            0.88  0.07 0.82 0.178 1.0
## recognizing     0.64  0.26 0.58 0.418 1.3
## communicating   0.37  0.43 0.42 0.584 2.0
## guilt           0.98 -0.15 0.88 0.119 1.0
## disrespected    0.94 -0.11 0.83 0.167 1.0
## free_will       0.43  0.43 0.49 0.512 2.0
## choices         0.30  0.61 0.58 0.419 1.5
## self_restraint  0.78  0.12 0.68 0.323 1.1
## intentions      0.40  0.51 0.55 0.450 1.9
## goal            0.32  0.54 0.50 0.501 1.6
## conscious       0.49  0.44 0.56 0.437 2.0
## self_aware      0.61  0.29 0.56 0.438 1.4
## desires         0.50  0.42 0.56 0.444 1.9
## embarrassed     1.00 -0.24 0.91 0.091 1.1
## emo_recog       0.94 -0.11 0.83 0.174 1.0
## joy             0.81  0.19 0.79 0.213 1.1
## morality        0.88 -0.08 0.74 0.262 1.0
## personality     0.83  0.08 0.73 0.265 1.0
## pleasure        0.49  0.51 0.66 0.339 2.0
## pride           0.96 -0.07 0.88 0.120 1.0
## 
##                         MR1  MR2
## SS loadings           16.98 9.30
## Proportion Var         0.42 0.23
## Cumulative Var         0.42 0.66
## Proportion Explained   0.65 0.35
## Cumulative Proportion  0.65 1.00
## 
##  With factor correlations of 
##      MR1  MR2
## MR1 1.00 0.32
## MR2 0.32 1.00
## 
## Mean item complexity =  1.3
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  69.39 with Chi Square of  12824.86
## The degrees of freedom for the model are 701  and the objective function was  31.95 
## 
## The root mean square of the residuals (RMSR) is  0.04 
## The df corrected root mean square of the residuals is  0.05 
## 
## The harmonic number of observations is  200 with the empirical chi square  612.68  with prob <  0.99 
## The total number of observations was  200  with MLE Chi Square =  5862.79  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.519
## RMSEA index =  0.201  and the 90 % confidence intervals are  0.187 NA
## BIC =  2148.67
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                MR1 MR2
## Correlation of scores with factors               1   1
## Multiple R square of scores with factors         1   1
## Minimum correlation of possible factor scores    1   1

Factor 1

Study 1, BEETLE condition: Rotated Factor 1

	F1
embarrassed	1.0020306
guilt	0.9756958
pride	0.9585644
disrespected	0.9411429
beliefs	0.9381816
emo_recog	0.9379207
depressed	0.9111360
love	0.8819231
morality	0.8808931
personality	0.8302287
computations	0.8119560
joy	0.8066930
reasoning	0.7847090
self_restraint	0.7753788
happy	0.7643661
thoughts	0.7127419
angry	0.6642971
recognizing	0.6378948
nauseated	0.6351466
self_aware	0.6084382
calm	0.5017369
desires	0.4969792
pleasure	0.4913029
conscious	0.4856901
free_will	0.4323001
safe	0.4101979
intentions	0.4028151
remembering	0.3865968
communicating	0.3661612
fear	0.3431680
goal	0.3180000
choices	0.3015613
tired	0.2552377
depth	0.1370655
pain	0.0272150
odors	-0.0512998
sounds	-0.0831009
temperature	-0.1504020
hungry	-0.2174591
seeing	-0.2201802

Factor 2

Study 1, BEETLE condition: Rotated Factor 2

	F2
hungry	0.9182565
seeing	0.8545007
temperature	0.8415400
pain	0.8117742
odors	0.7214288
sounds	0.7108432
tired	0.6524259
choices	0.6103512
depth	0.5833357
fear	0.5803580
goal	0.5378434
pleasure	0.5100210
intentions	0.5073046
calm	0.4981085
safe	0.4941841
remembering	0.4894506
conscious	0.4374112
free_will	0.4283789
communicating	0.4267743
desires	0.4200526
nauseated	0.3592218
self_aware	0.2853111
angry	0.2652646
recognizing	0.2623749
thoughts	0.2454170
happy	0.2314483
joy	0.1927156
reasoning	0.1755708
self_restraint	0.1230272
personality	0.0754739
love	0.0698322
depressed	0.0212097
pride	-0.0730489
morality	-0.0798466
disrespected	-0.1073581
emo_recog	-0.1093565
guilt	-0.1506505
beliefs	-0.1779520
computations	-0.2007574
embarrassed	-0.2392119

Factor 3 (not applicable)

EFA: ROBOT condition

Step 1: Determine how many factors to extract

Step 2: Run EFA without rotation

## The items do not have an equal number of response alternatives, global set to FALSE

## Factor Analysis using method =  minres
## Call: fa(r = d1_robot, nfactors = nfactors_d1_robot, rotate = "none", 
##     fm = "minres", cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   h2   u2 com
## happy           0.92 -0.01 0.85 0.15 1.0
## depressed       0.90 -0.11 0.82 0.18 1.0
## fear            0.89 -0.05 0.79 0.21 1.0
## angry           0.91  0.01 0.84 0.16 1.0
## calm            0.82  0.03 0.67 0.33 1.0
## sounds         -0.29  0.69 0.56 0.44 1.3
## seeing          0.00  0.79 0.63 0.37 1.0
## temperature    -0.17  0.76 0.61 0.39 1.1
## odors           0.17  0.56 0.34 0.66 1.2
## depth           0.07  0.70 0.50 0.50 1.0
## computations   -0.48  0.62 0.62 0.38 1.9
## thoughts        0.77  0.15 0.61 0.39 1.1
## reasoning       0.39  0.60 0.51 0.49 1.7
## remembering    -0.11  0.77 0.61 0.39 1.0
## beliefs         0.83  0.08 0.70 0.30 1.0
## hungry          0.89 -0.06 0.79 0.21 1.0
## tired           0.87  0.06 0.76 0.24 1.0
## pain            0.88 -0.04 0.77 0.23 1.0
## nauseated       0.88 -0.13 0.80 0.20 1.0
## safe            0.85  0.05 0.72 0.28 1.0
## love            0.92 -0.08 0.85 0.15 1.0
## recognizing     0.01  0.80 0.65 0.35 1.0
## communicating  -0.03  0.71 0.50 0.50 1.0
## guilt           0.87 -0.09 0.76 0.24 1.0
## disrespected    0.86 -0.06 0.75 0.25 1.0
## free_will       0.88  0.10 0.78 0.22 1.0
## choices         0.16  0.67 0.47 0.53 1.1
## self_restraint  0.69  0.25 0.54 0.46 1.3
## intentions      0.64  0.24 0.47 0.53 1.3
## goal            0.02  0.70 0.49 0.51 1.0
## conscious       0.81  0.04 0.65 0.35 1.0
## self_aware      0.77  0.17 0.63 0.37 1.1
## desires         0.89  0.10 0.80 0.20 1.0
## embarrassed     0.90 -0.09 0.82 0.18 1.0
## emo_recog       0.71  0.32 0.61 0.39 1.4
## joy             0.93  0.00 0.86 0.14 1.0
## morality        0.65  0.30 0.51 0.49 1.4
## personality     0.72  0.31 0.61 0.39 1.4
## pleasure        0.90 -0.05 0.81 0.19 1.0
## pride           0.88 -0.04 0.77 0.23 1.0
## 
##                         MR1  MR2
## SS loadings           20.36 6.48
## Proportion Var         0.51 0.16
## Cumulative Var         0.51 0.67
## Proportion Explained   0.76 0.24
## Cumulative Proportion  0.76 1.00
## 
## Mean item complexity =  1.1
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  45.84 with Chi Square of  8702.57
## The degrees of freedom for the model are 701  and the objective function was  5.26 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  205 with the empirical chi square  271.57  with prob <  1 
## The total number of observations was  205  with MLE Chi Square =  991.44  with prob <  2.5e-12 
## 
## Tucker Lewis Index of factoring reliability =  0.959
## RMSEA index =  0.051  and the 90 % confidence intervals are  0.038 0.051
## BIC =  -2739.99
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                 MR1  MR2
## Correlation of scores with factors             0.99 0.97
## Multiple R square of scores with factors       0.99 0.94
## Minimum correlation of possible factor scores  0.98 0.88

Step 3: Run EFA with oblimin rotation

## The items do not have an equal number of response alternatives, global set to FALSE

## Factor Analysis using method =  minres
## Call: fa(r = d1_robot, nfactors = nfactors_d1_robot, rotate = "oblimin", 
##     fm = "minres", cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   h2   u2 com
## happy           0.92 -0.03 0.85 0.15 1.0
## depressed       0.89 -0.13 0.82 0.18 1.0
## fear            0.89 -0.07 0.79 0.21 1.0
## angry           0.91 -0.01 0.84 0.16 1.0
## calm            0.82  0.01 0.67 0.33 1.0
## sounds         -0.27  0.70 0.56 0.44 1.3
## seeing          0.02  0.79 0.63 0.37 1.0
## temperature    -0.14  0.76 0.61 0.39 1.1
## odors           0.18  0.56 0.34 0.66 1.2
## depth           0.09  0.70 0.50 0.50 1.0
## computations   -0.46  0.63 0.62 0.38 1.8
## thoughts        0.77  0.13 0.61 0.39 1.1
## reasoning       0.40  0.59 0.51 0.49 1.8
## remembering    -0.09  0.77 0.61 0.39 1.0
## beliefs         0.83  0.06 0.70 0.30 1.0
## hungry          0.89 -0.08 0.79 0.21 1.0
## tired           0.87  0.04 0.76 0.24 1.0
## pain            0.88 -0.06 0.77 0.23 1.0
## nauseated       0.88 -0.15 0.80 0.20 1.1
## safe            0.85  0.03 0.72 0.28 1.0
## love            0.92 -0.10 0.85 0.15 1.0
## recognizing     0.04  0.80 0.65 0.35 1.0
## communicating  -0.01  0.71 0.50 0.50 1.0
## guilt           0.87 -0.11 0.76 0.24 1.0
## disrespected    0.86 -0.08 0.75 0.25 1.0
## free_will       0.88  0.08 0.78 0.22 1.0
## choices         0.19  0.66 0.47 0.53 1.2
## self_restraint  0.70  0.24 0.54 0.46 1.2
## intentions      0.65  0.23 0.47 0.53 1.2
## goal            0.04  0.70 0.49 0.51 1.0
## conscious       0.81  0.02 0.65 0.35 1.0
## self_aware      0.78  0.16 0.63 0.37 1.1
## desires         0.89  0.08 0.80 0.20 1.0
## embarrassed     0.90 -0.11 0.82 0.18 1.0
## emo_recog       0.72  0.30 0.61 0.39 1.3
## joy             0.93 -0.02 0.86 0.14 1.0
## morality        0.66  0.28 0.51 0.49 1.4
## personality     0.73  0.29 0.61 0.39 1.3
## pleasure        0.90 -0.08 0.81 0.19 1.0
## pride           0.87 -0.06 0.77 0.23 1.0
## 
##                         MR1  MR2
## SS loadings           20.38 6.45
## Proportion Var         0.51 0.16
## Cumulative Var         0.51 0.67
## Proportion Explained   0.76 0.24
## Cumulative Proportion  0.76 1.00
## 
##  With factor correlations of 
##       MR1   MR2
## MR1  1.00 -0.01
## MR2 -0.01  1.00
## 
## Mean item complexity =  1.1
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  45.84 with Chi Square of  8702.57
## The degrees of freedom for the model are 701  and the objective function was  5.26 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  205 with the empirical chi square  271.57  with prob <  1 
## The total number of observations was  205  with MLE Chi Square =  991.44  with prob <  2.5e-12 
## 
## Tucker Lewis Index of factoring reliability =  0.959
## RMSEA index =  0.051  and the 90 % confidence intervals are  0.038 0.051
## BIC =  -2739.99
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                 MR1  MR2
## Correlation of scores with factors             0.99 0.97
## Multiple R square of scores with factors       0.99 0.94
## Minimum correlation of possible factor scores  0.98 0.88

Factor 1

Study 1, ROBOT condition: Rotated Factor 1

	F1
joy	0.9268304
happy	0.9227355
love	0.9172755
angry	0.9147543
pleasure	0.8971716
embarrassed	0.8951784
desires	0.8934416
depressed	0.8926710
hungry	0.8869347
fear	0.8853683
free_will	0.8818153
nauseated	0.8797621
pain	0.8757508
pride	0.8747875
tired	0.8736116
guilt	0.8655426
disrespected	0.8613605
safe	0.8491077
beliefs	0.8337374
calm	0.8185905
conscious	0.8077695
self_aware	0.7765436
thoughts	0.7704208
personality	0.7290145
emo_recog	0.7197687
self_restraint	0.7007173
morality	0.6590832
intentions	0.6487046
reasoning	0.4046202
choices	0.1856162
odors	0.1831300
depth	0.0926194
goal	0.0426467
recognizing	0.0368066
seeing	0.0211872
communicating	-0.0081716
remembering	-0.0880354
temperature	-0.1433794
sounds	-0.2684681
computations	-0.4601106

Factor 2

Study 1, ROBOT condition: Rotated Factor 2

	F2
recognizing	0.8042954
seeing	0.7944824
remembering	0.7735647
temperature	0.7644937
communicating	0.7091134
depth	0.7031083
goal	0.6968370
sounds	0.6961599
choices	0.6621298
computations	0.6318591
reasoning	0.5894337
odors	0.5553435
emo_recog	0.3024544
personality	0.2910713
morality	0.2819530
self_restraint	0.2367662
intentions	0.2295320
self_aware	0.1558897
thoughts	0.1348547
desires	0.0795178
free_will	0.0769316
beliefs	0.0645677
tired	0.0415599
safe	0.0267561
conscious	0.0169271
calm	0.0142140
angry	-0.0115489
joy	-0.0178925
happy	-0.0348767
pride	-0.0601179
pain	-0.0647785
fear	-0.0684792
pleasure	-0.0752471
hungry	-0.0763915
disrespected	-0.0768476
love	-0.1045010
embarrassed	-0.1110573
guilt	-0.1110947
depressed	-0.1274261
nauseated	-0.1547037

Factor 3 (not applicable)

EFA: ALL conditions

Step 1: Determine how many factors to extract

Step 2: Run EFA without rotation

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Factor Analysis using method =  minres
## Call: fa(r = d1_all, nfactors = nfactors_d1_all, rotate = "none", fm = "minres", 
##     cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   MR3   h2    u2 com
## happy           0.91 -0.09 -0.08 0.85 0.155 1.0
## depressed       0.90 -0.03 -0.27 0.88 0.119 1.2
## fear            0.83 -0.36  0.21 0.86 0.136 1.5
## angry           0.88 -0.14 -0.04 0.79 0.207 1.1
## calm            0.85 -0.15  0.11 0.75 0.246 1.1
## sounds          0.13  0.55  0.54 0.61 0.395 2.1
## seeing          0.38  0.28  0.71 0.74 0.262 1.9
## temperature     0.25  0.46  0.66 0.71 0.290 2.1
## odors           0.46  0.10  0.60 0.58 0.418 2.0
## depth           0.32  0.54  0.40 0.55 0.450 2.5
## computations   -0.27  0.88 -0.27 0.91 0.085 1.4
## thoughts        0.86  0.01 -0.04 0.74 0.264 1.0
## reasoning       0.52  0.65 -0.11 0.71 0.293 2.0
## remembering     0.17  0.80  0.18 0.69 0.305 1.2
## beliefs         0.76  0.23 -0.42 0.80 0.198 1.8
## hungry          0.68 -0.56  0.43 0.97 0.033 2.7
## tired           0.81 -0.34  0.28 0.84 0.157 1.6
## pain            0.75 -0.48  0.36 0.93 0.074 2.2
## nauseated       0.87 -0.21  0.05 0.81 0.186 1.1
## safe            0.83 -0.22  0.15 0.75 0.246 1.2
## love            0.91  0.01 -0.25 0.89 0.111 1.2
## recognizing     0.21  0.86 -0.02 0.79 0.208 1.1
## communicating   0.30  0.68  0.18 0.58 0.416 1.6
## guilt           0.85  0.03 -0.39 0.88 0.121 1.4
## disrespected    0.84  0.06 -0.36 0.84 0.160 1.4
## free_will       0.82 -0.27  0.13 0.77 0.232 1.3
## choices         0.51  0.41  0.34 0.55 0.451 2.7
## self_restraint  0.75  0.24 -0.13 0.63 0.366 1.3
## intentions      0.76 -0.02  0.13 0.60 0.402 1.1
## goal            0.37  0.55  0.30 0.54 0.464 2.4
## conscious       0.83 -0.22  0.13 0.75 0.251 1.2
## self_aware      0.82 -0.02  0.01 0.67 0.331 1.0
## desires         0.85 -0.21  0.11 0.78 0.223 1.2
## embarrassed     0.84  0.07 -0.45 0.91 0.087 1.6
## emo_recog       0.70  0.40 -0.33 0.76 0.235 2.1
## joy             0.92 -0.05 -0.12 0.86 0.141 1.0
## morality        0.60  0.47 -0.35 0.70 0.305 2.6
## personality     0.77  0.30 -0.21 0.73 0.271 1.5
## pleasure        0.88 -0.25  0.13 0.85 0.150 1.2
## pride           0.87  0.08 -0.35 0.89 0.112 1.3
## 
##                         MR1  MR2  MR3
## SS loadings           20.38 6.18 3.89
## Proportion Var         0.51 0.15 0.10
## Cumulative Var         0.51 0.66 0.76
## Proportion Explained   0.67 0.20 0.13
## Cumulative Proportion  0.67 0.87 1.00
## 
## Mean item complexity =  1.6
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  96.01 with Chi Square of  37427.06
## The degrees of freedom for the model are 663  and the objective function was  46.82 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  405 with the empirical chi square  496.78  with prob <  1 
## The total number of observations was  405  with MLE Chi Square =  18159.94  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.435
## RMSEA index =  0.261  and the 90 % confidence intervals are  0.252 NA
## BIC =  14179.37
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                MR1 MR2 MR3
## Correlation of scores with factors               1   1   1
## Multiple R square of scores with factors         1   1   1
## Minimum correlation of possible factor scores    1   1   1

Step 3: Run EFA with oblimin rotation

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate =
## rotate, : A Heywood case was detected. Examine the loadings carefully.

## Factor Analysis using method =  minres
## Call: fa(r = d1_all, nfactors = nfactors_d1_all, rotate = "oblimin", 
##     fm = "minres", cor = "poly")
## 
##  Warning: A Heywood case was detected. 
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   MR3   h2    u2 com
## happy           0.74  0.35  0.04 0.85 0.155 1.4
## depressed       0.89  0.18 -0.07 0.88 0.119 1.1
## fear            0.40  0.71  0.09 0.86 0.136 1.6
## angry           0.67  0.40  0.04 0.79 0.207 1.6
## calm            0.53  0.49  0.14 0.75 0.246 2.1
## sounds         -0.22 -0.03  0.81 0.61 0.395 1.1
## seeing         -0.21  0.37  0.83 0.74 0.262 1.5
## temperature    -0.23  0.15  0.88 0.71 0.290 1.2
## odors          -0.09  0.47  0.63 0.58 0.418 1.9
## depth           0.04 -0.05  0.73 0.55 0.450 1.0
## computations    0.17 -0.94  0.31 0.91 0.085 1.3
## thoughts        0.68  0.28  0.13 0.74 0.264 1.4
## reasoning       0.61 -0.37  0.43 0.71 0.293 2.5
## remembering     0.14 -0.43  0.70 0.69 0.305 1.8
## beliefs         0.95 -0.17 -0.04 0.80 0.198 1.1
## hungry          0.07  0.95  0.10 0.97 0.033 1.0
## tired           0.33  0.73  0.15 0.84 0.157 1.5
## pain            0.19  0.87  0.12 0.93 0.074 1.1
## nauseated       0.58  0.51  0.06 0.81 0.186 2.0
## safe            0.47  0.56  0.13 0.75 0.246 2.1
## love            0.89  0.16 -0.03 0.89 0.111 1.1
## recognizing     0.34 -0.59  0.59 0.79 0.208 2.6
## communicating   0.22 -0.29  0.65 0.58 0.416 1.6
## guilt           0.95  0.04 -0.13 0.88 0.121 1.0
## disrespected    0.93  0.03 -0.09 0.84 0.160 1.0
## free_will       0.47  0.58  0.08 0.77 0.232 2.0
## choices         0.21  0.08  0.64 0.55 0.451 1.3
## self_restraint  0.72  0.00  0.19 0.63 0.366 1.1
## intentions      0.47  0.38  0.23 0.60 0.402 2.4
## goal            0.15 -0.09  0.67 0.54 0.464 1.1
## conscious       0.48  0.55  0.11 0.75 0.251 2.1
## self_aware      0.61  0.32  0.15 0.67 0.331 1.7
## desires         0.52  0.54  0.11 0.78 0.223 2.1
## embarrassed     1.00 -0.04 -0.16 0.91 0.087 1.1
## emo_recog       0.87 -0.26  0.13 0.76 0.235 1.2
## joy             0.78  0.29  0.04 0.86 0.141 1.3
## morality        0.81 -0.36  0.14 0.70 0.305 1.4
## personality     0.81 -0.08  0.17 0.73 0.271 1.1
## pleasure        0.52  0.59  0.10 0.85 0.150 2.0
## pride           0.95  0.03 -0.07 0.89 0.112 1.0
## 
##                         MR1  MR2  MR3
## SS loadings           15.56 8.67 6.22
## Proportion Var         0.39 0.22 0.16
## Cumulative Var         0.39 0.61 0.76
## Proportion Explained   0.51 0.28 0.20
## Cumulative Proportion  0.51 0.80 1.00
## 
##  With factor correlations of 
##      MR1  MR2  MR3
## MR1 1.00 0.31 0.30
## MR2 0.31 1.00 0.03
## MR3 0.30 0.03 1.00
## 
## Mean item complexity =  1.5
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  96.01 with Chi Square of  37427.06
## The degrees of freedom for the model are 663  and the objective function was  46.82 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  405 with the empirical chi square  496.78  with prob <  1 
## The total number of observations was  405  with MLE Chi Square =  18159.94  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.435
## RMSEA index =  0.261  and the 90 % confidence intervals are  0.252 NA
## BIC =  14179.37
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                MR1 MR2 MR3
## Correlation of scores with factors               1   1   1
## Multiple R square of scores with factors         1   1   1
## Minimum correlation of possible factor scores    1   1   1

Factor 1

Study 1, ALL conditions: Rotated Factor 1

	F1
embarrassed	1.0039171
guilt	0.9549394
pride	0.9500095
beliefs	0.9457640
disrespected	0.9287591
love	0.8887752
depressed	0.8867765
emo_recog	0.8687846
morality	0.8139255
personality	0.8072699
joy	0.7808125
happy	0.7355395
self_restraint	0.7183893
thoughts	0.6795263
angry	0.6699291
reasoning	0.6100538
self_aware	0.6066399
nauseated	0.5820576
calm	0.5273982
desires	0.5168242
pleasure	0.5167804
conscious	0.4843874
free_will	0.4721601
intentions	0.4716231
safe	0.4693872
fear	0.3954898
recognizing	0.3390921
tired	0.3279838
communicating	0.2174309
choices	0.2085833
pain	0.1948848
computations	0.1749238
goal	0.1538601
remembering	0.1436317
hungry	0.0676230
depth	0.0357794
odors	-0.0928651
seeing	-0.2092235
sounds	-0.2167295
temperature	-0.2329065

Factor 2

Study 1, ALL conditions: Rotated Factor 2

	F2
hungry	0.9497507
pain	0.8661138
tired	0.7259825
fear	0.7091336
pleasure	0.5903341
free_will	0.5848985
safe	0.5601083
conscious	0.5483455
desires	0.5371240
nauseated	0.5128479
calm	0.4933901
odors	0.4665908
angry	0.4007333
intentions	0.3772565
seeing	0.3743087
happy	0.3509515
self_aware	0.3179769
joy	0.2913976
thoughts	0.2835311
depressed	0.1778244
love	0.1614489
temperature	0.1537143
choices	0.0842398
guilt	0.0414608
pride	0.0343239
disrespected	0.0313665
self_restraint	0.0004561
sounds	-0.0312768
embarrassed	-0.0398313
depth	-0.0454765
personality	-0.0842118
goal	-0.0928145
beliefs	-0.1676734
emo_recog	-0.2599410
communicating	-0.2887804
morality	-0.3610688
reasoning	-0.3735732
remembering	-0.4319721
recognizing	-0.5913187
computations	-0.9356737

Factor 3

Study 1, ALL conditions: Rotated Factor 3

	F3
temperature	0.8776676
seeing	0.8298053
sounds	0.8133531
depth	0.7305012
remembering	0.6954912
goal	0.6736999
communicating	0.6466134
choices	0.6352751
odors	0.6322865
recognizing	0.5921749
reasoning	0.4312595
computations	0.3079231
intentions	0.2293126
self_restraint	0.1881600
personality	0.1709402
tired	0.1534729
self_aware	0.1504231
calm	0.1443969
morality	0.1376083
thoughts	0.1332763
safe	0.1291031
emo_recog	0.1279594
pain	0.1173019
conscious	0.1131094
desires	0.1095156
hungry	0.1039194
pleasure	0.1015095
fear	0.0852748
free_will	0.0794852
nauseated	0.0622208
joy	0.0435816
happy	0.0421713
angry	0.0385833
love	-0.0304607
beliefs	-0.0436463
pride	-0.0702958
depressed	-0.0722487
disrespected	-0.0882474
guilt	-0.1323865
embarrassed	-0.1626738

Predict latent variable structure for CFA in follow-up studies

Extract latent variable structure

## Joining by: "order"
## Joining by: "order"

Study 1: Factor structure

order	mc_MR1	loading_MR1	mc_MR2	loading_MR2	mc_MR3	loading_MR3
1	embarrassed	1.00	hungry	0.95	temperature	0.88
2	guilt	0.95	pain	0.87	seeing	0.83
3	pride	0.95	tired	0.73	sounds	0.81
4	beliefs	0.95	fear	0.71	depth	0.73
5	disrespected	0.93	pleasure	0.59	remembering	0.70
6	love	0.89	free_will	0.58	goal	0.67
7	depressed	0.89	safe	0.56	communicating	0.65
8	emo_recog	0.87	conscious	0.55	choices	0.64
9	morality	0.81	desires	0.54	odors	0.63
10	personality	0.81	NA	NA	recognizing	0.59
11	joy	0.78	NA	NA	computations	0.31
12	happy	0.74	NA	NA	NA	NA
13	self_restraint	0.72	NA	NA	NA	NA
14	thoughts	0.68	NA	NA	NA	NA
15	angry	0.67	NA	NA	NA	NA
16	reasoning	0.61	NA	NA	NA	NA
17	self_aware	0.61	NA	NA	NA	NA
18	nauseated	0.58	NA	NA	NA	NA
19	calm	0.53	NA	NA	NA	NA
20	intentions	0.47	NA	NA	NA	NA

ModelDD: Data-driven, three factors (MR1, MR2, MR3; see Study 1)

## lavaan (0.5-20) converged normally after  69 iterations
## 
##   Number of observations                           405
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             4126.942
##   Degrees of freedom                               737
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            14736.878
##   Degrees of freedom                               780
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.757
##   Tucker-Lewis Index (TLI)                       0.743
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -27119.488
##   Loglikelihood unrestricted model (H1)     -25056.016
## 
##   Number of free parameters                         83
##   Akaike (AIC)                               54404.975
##   Bayesian (BIC)                             54737.298
##   Sample-size adjusted Bayesian (BIC)        54473.928
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.107
##   90 Percent Confidence Interval          0.103  0.110
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.140
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   MR1 =~                                              
##     embarrassed       1.000                           
##     guilt             0.949    0.049   19.313    0.000
##     pride             1.225    0.058   21.216    0.000
##     beliefs           1.024    0.064   16.080    0.000
##     disrespected      1.032    0.055   18.686    0.000
##     love              1.402    0.064   22.035    0.000
##     depressed         1.225    0.058   21.205    0.000
##     emo_recog         1.105    0.075   14.816    0.000
##     morality          0.901    0.078   11.474    0.000
##     personality       1.254    0.076   16.461    0.000
##     joy               1.549    0.072   21.598    0.000
##     happy             1.511    0.073   20.774    0.000
##     self_restraint    1.124    0.081   13.893    0.000
##     thoughts          1.443    0.083   17.433    0.000
##     angry             1.460    0.079   18.592    0.000
##     reasoning         0.944    0.100    9.403    0.000
##     self_aware        1.349    0.085   15.840    0.000
##     nauseated         1.257    0.072   17.563    0.000
##     calm              1.433    0.091   15.702    0.000
##     intentions        1.294    0.100   12.920    0.000
##   MR2 =~                                              
##     hungry            1.000                           
##     pain              0.960    0.040   23.921    0.000
##     tired             0.836    0.037   22.617    0.000
##     fear              0.888    0.038   23.317    0.000
##     pleasure          0.735    0.033   22.274    0.000
##     free_will         0.732    0.038   19.316    0.000
##     safe              0.730    0.037   19.598    0.000
##     conscious         0.724    0.037   19.447    0.000
##     desires           0.726    0.036   20.039    0.000
##   MR3 =~                                              
##     temperature       1.000                           
##     seeing            1.022    0.096   10.636    0.000
##     sounds            0.848    0.081   10.511    0.000
##     depth             1.172    0.106   11.085    0.000
##     remembering       1.318    0.107   12.275    0.000
##     goal              1.182    0.106   11.141    0.000
##     communicating     1.141    0.097   11.782    0.000
##     choices           1.080    0.100   10.792    0.000
##     odors             0.824    0.102    8.096    0.000
##     recognizing       1.326    0.109   12.212    0.000
##     computations      0.936    0.127    7.374    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   MR1 ~~                                              
##     MR2               1.500    0.148   10.137    0.000
##     MR3               0.339    0.064    5.274    0.000
##   MR2 ~~                                              
##     MR3               0.408    0.140    2.911    0.004
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     embarrassed       0.465    0.035   13.421    0.000
##     guilt             0.409    0.031   13.402    0.000
##     pride             0.444    0.034   12.958    0.000
##     beliefs           0.905    0.066   13.795    0.000
##     disrespected      0.551    0.041   13.503    0.000
##     love              0.472    0.037   12.662    0.000
##     depressed         0.446    0.034   12.962    0.000
##     emo_recog         1.345    0.097   13.889    0.000
##     morality          1.741    0.124   14.055    0.000
##     personality       1.261    0.092   13.762    0.000
##     joy               0.646    0.050   12.831    0.000
##     happy             0.752    0.057   13.086    0.000
##     self_restraint    1.662    0.119   13.945    0.000
##     thoughts          1.383    0.101   13.664    0.000
##     angry             1.124    0.083   13.517    0.000
##     reasoning         3.056    0.216   14.121    0.000
##     self_aware        1.645    0.119   13.814    0.000
##     nauseated         1.023    0.075   13.650    0.000
##     calm              1.905    0.138   13.825    0.000
##     intentions        2.669    0.191   13.995    0.000
##     hungry            2.011    0.158   12.754    0.000
##     pain              1.138    0.096   11.821    0.000
##     tired             1.139    0.092   12.405    0.000
##     fear              1.112    0.092   12.120    0.000
##     pleasure          0.942    0.075   12.526    0.000
##     free_will         1.607    0.121   13.243    0.000
##     safe              1.519    0.115   13.192    0.000
##     conscious         1.538    0.116   13.220    0.000
##     desires           1.391    0.106   13.108    0.000
##     temperature       1.780    0.139   12.833    0.000
##     seeing            2.324    0.177   13.113    0.000
##     sounds            1.671    0.127   13.161    0.000
##     depth             2.606    0.202   12.919    0.000
##     remembering       2.071    0.171   12.140    0.000
##     goal              2.595    0.201   12.892    0.000
##     communicating     1.898    0.152   12.524    0.000
##     choices           2.453    0.188   13.050    0.000
##     odors             3.535    0.257   13.755    0.000
##     recognizing       2.154    0.177   12.196    0.000
##     computations      5.831    0.421   13.859    0.000
##     MR1               0.876    0.089    9.826    0.000
##     MR2               4.852    0.466   10.404    0.000
##     MR3               1.299    0.186    6.968    0.000

ModelWDM: Theoretical, three factors (AFFECT, AUTONOMY, PERCEPTION; see Weisman et al., 2015)

## lavaan (0.5-20) converged normally after  45 iterations
## 
##   Number of observations                           405
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              619.030
##   Degrees of freedom                               101
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             3817.954
##   Degrees of freedom                               120
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.860
##   Tucker-Lewis Index (TLI)                       0.834
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -11579.778
##   Loglikelihood unrestricted model (H1)     -11270.263
## 
##   Number of free parameters                         35
##   Akaike (AIC)                               23229.557
##   Bayesian (BIC)                             23369.693
##   Sample-size adjusted Bayesian (BIC)        23258.633
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.113
##   90 Percent Confidence Interval          0.104  0.121
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.094
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   affect =~                                           
##     happy             1.000                           
##     depressed         0.712    0.032   22.463    0.000
##     fear              1.064    0.058   18.257    0.000
##     angry             0.939    0.041   23.042    0.000
##     calm              0.957    0.049   19.501    0.000
##     joy               0.988    0.035   28.454    0.000
##   perception =~                                       
##     sounds            1.000                           
##     seeing            1.393    0.121   11.506    0.000
##     temperature       1.304    0.112   11.665    0.000
##     odors             1.299    0.126   10.275    0.000
##     depth             1.228    0.125    9.856    0.000
##   autonomy =~                                         
##     free_will         1.000                           
##     choices           0.699    0.067   10.466    0.000
##     self_restraint    0.661    0.055   11.924    0.000
##     intentions        0.952    0.067   14.196    0.000
##     goal              0.586    0.071    8.261    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   affect ~~                                           
##     perception        0.461    0.096    4.820    0.000
##     autonomy          2.026    0.189   10.693    0.000
##   perception ~~                                       
##     autonomy          0.855    0.124    6.880    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     happy             0.475    0.047   10.057    0.000
##     depressed         0.607    0.048   12.601    0.000
##     fear              2.362    0.178   13.302    0.000
##     angry             0.982    0.079   12.472    0.000
##     calm              1.617    0.123   13.130    0.000
##     joy               0.523    0.050   10.520    0.000
##     sounds            1.557    0.128   12.202    0.000
##     seeing            1.648    0.158   10.461    0.000
##     temperature       1.297    0.129   10.041    0.000
##     odors             2.647    0.217   12.217    0.000
##     depth             2.810    0.224   12.542    0.000
##     free_will         1.819    0.159   11.403    0.000
##     choices           2.802    0.209   13.400    0.000
##     self_restraint    1.726    0.133   13.007    0.000
##     intentions        1.970    0.165   11.909    0.000
##     goal              3.589    0.260   13.780    0.000
##     affect            2.277    0.193   11.775    0.000
##     perception        1.048    0.161    6.519    0.000
##     autonomy          2.387    0.283    8.433    0.000

ModelGGW: Theoretical, two factors (AGENCY, EXPERIENCE; see Gray et al., 2007)

## lavaan (0.5-20) converged normally after  43 iterations
## 
##   Number of observations                           405
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             1816.523
##   Degrees of freedom                               134
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             5604.203
##   Degrees of freedom                               153
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.691
##   Tucker-Lewis Index (TLI)                       0.648
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -12787.515
##   Loglikelihood unrestricted model (H1)     -11879.253
## 
##   Number of free parameters                         37
##   Akaike (AIC)                               25649.030
##   Bayesian (BIC)                             25797.174
##   Sample-size adjusted Bayesian (BIC)        25679.768
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.176
##   90 Percent Confidence Interval          0.169  0.183
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.147
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   experience =~                                       
##     hungry            1.000                           
##     fear              0.989    0.060   16.405    0.000
##     pain              1.002    0.064   15.593    0.000
##     pleasure          0.882    0.051   17.236    0.000
##     angry             0.752    0.047   16.016    0.000
##     desires           0.879    0.054   16.302    0.000
##     personality       0.512    0.044   11.582    0.000
##     conscious         0.856    0.055   15.606    0.000
##     pride             0.496    0.036   13.749    0.000
##     embarrassed       0.384    0.032   12.178    0.000
##     joy               0.713    0.045   15.859    0.000
##   agency =~                                           
##     self_restraint    1.000                           
##     morality          0.818    0.068   12.040    0.000
##     remembering       0.592    0.090    6.538    0.000
##     emo_recog         0.924    0.068   13.662    0.000
##     goal              0.744    0.091    8.155    0.000
##     communicating     0.678    0.082    8.239    0.000
##     thoughts          1.075    0.078   13.787    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   experience ~~                                       
##     agency            1.599    0.185    8.661    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     hungry            3.374    0.251   13.433    0.000
##     fear              1.525    0.122   12.496    0.000
##     pain              2.102    0.162   12.941    0.000
##     pleasure          0.845    0.072   11.739    0.000
##     angry             1.020    0.080   12.734    0.000
##     desires           1.253    0.100   12.564    0.000
##     personality       1.724    0.125   13.822    0.000
##     conscious         1.526    0.118   12.935    0.000
##     pride             0.902    0.067   13.497    0.000
##     embarrassed       0.828    0.060   13.752    0.000
##     joy               0.971    0.076   12.816    0.000
##     self_restraint    1.245    0.112   11.150    0.000
##     morality          1.434    0.115   12.455    0.000
##     remembering       3.795    0.273   13.883    0.000
##     emo_recog         1.115    0.099   11.292    0.000
##     goal              3.566    0.261   13.645    0.000
##     communicating     2.889    0.212   13.630    0.000
##     thoughts          1.445    0.130   11.162    0.000
##     experience        3.488    0.428    8.149    0.000
##     agency            1.523    0.187    8.139    0.000

Compare models (if possible)

# compare models (iff continuous and ML)
customVuong(d1_all_fitDD, d1_all_fitWDM, d1_all_fitGGW)

## $mod1_v_mod2
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 116.327,   p = <2e-16
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -71.594,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -71.594,   p = < 2.2e-16
## 
## $mod1_v_mod3
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 70.002,   p = <2e-16
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -85.118,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -85.118,   p = < 2.2e-16
## 
## $mod3_v_mod2
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 26.088,   p = <2e-16
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -11.750,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -11.750,   p = < 2.2e-16
## 
## $winner
## [1] "WDM"

Study 2 (2016-01-12, 2 conditions, between-subjects - REPLICATION)

Demographics

Study 2: Exclusion

did_not_finish	failed_catch_trial	did_not_provide_yob	too_young	TOTAL_excluded	TOTAL_participated	OVERALL_TOTAL
0	0	13	0	13	406	419

Study 2: Sample size

condition	n
beetle	202
robot	204
all	406

Study 2: Study duration (minutes)

condition	min_duration	max_duration	median_duration	mean_duration	sd_duration
beetle	0.92	28.95	2.69	3.54	3.17
robot	1.00	16.72	2.52	3.18	2.17
all	0.92	28.95	2.63	3.36	2.72

## Joining by: c("condition", "min_age", "max_age", "median_age", "mean_age", "sd_age")

## Warning: joining character vector and factor, coercing into character
## vector

Study 2: Participant age (years; approximate)

condition	min_age	max_age	median_age	mean_age	sd_age
beetle	20	70	32	34.95	10.99
robot	20	70	33	35.60	10.92
all	20	70	33	35.28	10.95

Study 2: Participant gender

condition	m	f	other
beetle	93	108	1
robot	106	97	1
all	199	205	2

Study 2: Participant race/ethnicity

condition	asian_east	asian_south	black	hispanic	middle_eastern	multiracial	native_american	other_prefno	pac_islander	white
beetle	8	7	12	11	0	3	1	1	0	159
robot	14	1	14	10	1	5	1	2	1	155
all	22	8	26	21	1	8	2	3	1	314

Study 2: Participant religion

condition	buddhism	christianity	hinduism	islam	judaism	multireligious	none	other	other_prefno
beetle	6	80	1	3	5	1	95	6	5
robot	3	85	0	2	2	1	105	4	2
all	9	165	1	5	7	2	200	10	7

Exploratory factor analysis

EFA: BEETLE condition

Step 1: Determine how many factors to extract

Step 2: Run EFA without rotation

## The items do not have an equal number of response alternatives, global set to FALSE

## Factor Analysis using method =  minres
## Call: fa(r = d2_beetle, nfactors = nfactors_d2_beetle, rotate = "none", 
##     fm = "minres", cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   h2   u2 com
## happy           0.83  0.05 0.69 0.31 1.0
## depressed       0.81 -0.22 0.70 0.30 1.1
## fear            0.52  0.50 0.52 0.48 2.0
## angry           0.70  0.07 0.49 0.51 1.0
## calm            0.72  0.27 0.59 0.41 1.3
## sounds          0.28  0.71 0.58 0.42 1.3
## seeing          0.19  0.75 0.60 0.40 1.1
## temperature     0.12  0.71 0.52 0.48 1.1
## odors           0.20  0.69 0.52 0.48 1.2
## depth           0.39  0.38 0.29 0.71 2.0
## computations    0.62 -0.30 0.48 0.52 1.5
## thoughts        0.75  0.12 0.58 0.42 1.0
## reasoning       0.71 -0.11 0.52 0.48 1.0
## remembering     0.57  0.30 0.42 0.58 1.5
## beliefs         0.67 -0.38 0.60 0.40 1.6
## hungry         -0.02  0.75 0.57 0.43 1.0
## tired           0.48  0.54 0.53 0.47 2.0
## pain            0.32  0.64 0.52 0.48 1.5
## nauseated       0.67  0.07 0.46 0.54 1.0
## safe            0.59  0.37 0.49 0.51 1.7
## love            0.79 -0.23 0.68 0.32 1.2
## recognizing     0.70  0.05 0.50 0.50 1.0
## communicating   0.45  0.55 0.51 0.49 1.9
## guilt           0.73 -0.46 0.74 0.26 1.7
## disrespected    0.72 -0.40 0.68 0.32 1.6
## free_will       0.48  0.43 0.41 0.59 2.0
## choices         0.54  0.50 0.54 0.46 2.0
## self_restraint  0.74 -0.21 0.59 0.41 1.2
## intentions      0.51  0.46 0.47 0.53 2.0
## goal            0.46  0.50 0.46 0.54 2.0
## conscious       0.49  0.46 0.45 0.55 2.0
## self_aware      0.73  0.11 0.54 0.46 1.0
## desires         0.69  0.21 0.52 0.48 1.2
## embarrassed     0.68 -0.47 0.69 0.31 1.8
## emo_recog       0.84 -0.21 0.74 0.26 1.1
## joy             0.79  0.03 0.63 0.37 1.0
## morality        0.70 -0.42 0.67 0.33 1.6
## personality     0.83 -0.02 0.70 0.30 1.0
## pleasure        0.71  0.24 0.56 0.44 1.2
## pride           0.72 -0.38 0.67 0.33 1.5
## 
##                         MR1  MR2
## SS loadings           15.47 6.92
## Proportion Var         0.39 0.17
## Cumulative Var         0.39 0.56
## Proportion Explained   0.69 0.31
## Cumulative Proportion  0.69 1.00
## 
## Mean item complexity =  1.4
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  32.41 with Chi Square of  6055.74
## The degrees of freedom for the model are 701  and the objective function was  5.07 
## 
## The root mean square of the residuals (RMSR) is  0.04 
## The df corrected root mean square of the residuals is  0.04 
## 
## The harmonic number of observations is  202 with the empirical chi square  492.2  with prob <  1 
## The total number of observations was  202  with MLE Chi Square =  940.72  with prob <  3.2e-09 
## 
## Tucker Lewis Index of factoring reliability =  0.949
## RMSEA index =  0.048  and the 90 % confidence intervals are  0.034 0.048
## BIC =  -2780.37
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                 MR1  MR2
## Correlation of scores with factors             0.99 0.97
## Multiple R square of scores with factors       0.98 0.94
## Minimum correlation of possible factor scores  0.95 0.88

Step 3: Run EFA with oblimin rotation

## The items do not have an equal number of response alternatives, global set to FALSE

## Factor Analysis using method =  minres
## Call: fa(r = d2_beetle, nfactors = nfactors_d2_beetle, rotate = "oblimin", 
##     fm = "minres", cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   h2   u2 com
## happy           0.70  0.32 0.69 0.31 1.4
## depressed       0.83  0.04 0.70 0.30 1.0
## fear            0.20  0.65 0.52 0.48 1.2
## angry           0.58  0.29 0.49 0.51 1.5
## calm            0.50  0.49 0.59 0.41 2.0
## sounds         -0.12  0.78 0.58 0.42 1.0
## seeing         -0.22  0.79 0.60 0.40 1.2
## temperature    -0.26  0.73 0.52 0.48 1.3
## odors          -0.18  0.74 0.52 0.48 1.1
## depth           0.15  0.49 0.29 0.71 1.2
## computations    0.71 -0.10 0.48 0.52 1.0
## thoughts        0.60  0.35 0.58 0.42 1.6
## reasoning       0.68  0.12 0.52 0.48 1.1
## remembering     0.35  0.47 0.42 0.58 1.9
## beliefs         0.79 -0.16 0.60 0.40 1.1
## hungry         -0.40  0.73 0.57 0.43 1.6
## tired           0.15  0.68 0.53 0.47 1.1
## pain           -0.05  0.73 0.52 0.48 1.0
## nauseated       0.56  0.28 0.46 0.54 1.5
## safe            0.33  0.55 0.49 0.51 1.6
## love            0.82  0.03 0.68 0.32 1.0
## recognizing     0.60  0.27 0.50 0.50 1.4
## communicating   0.12  0.68 0.51 0.49 1.1
## guilt           0.88 -0.22 0.74 0.26 1.1
## disrespected    0.84 -0.16 0.68 0.32 1.1
## free_will       0.20  0.57 0.41 0.59 1.2
## choices         0.22  0.65 0.54 0.46 1.2
## self_restraint  0.76  0.03 0.59 0.41 1.0
## intentions      0.21  0.61 0.47 0.53 1.2
## goal            0.15  0.63 0.46 0.54 1.1
## conscious       0.20  0.60 0.45 0.55 1.2
## self_aware      0.58  0.34 0.54 0.46 1.6
## desires         0.50  0.43 0.52 0.48 2.0
## embarrassed     0.85 -0.24 0.69 0.31 1.2
## emo_recog       0.85  0.06 0.74 0.26 1.0
## joy             0.68  0.28 0.63 0.37 1.3
## morality        0.84 -0.19 0.67 0.33 1.1
## personality     0.75  0.24 0.70 0.30 1.2
## pleasure        0.50  0.46 0.56 0.44 2.0
## pride           0.84 -0.14 0.67 0.33 1.1
## 
##                         MR1  MR2
## SS loadings           13.07 9.32
## Proportion Var         0.33 0.23
## Cumulative Var         0.33 0.56
## Proportion Explained   0.58 0.42
## Cumulative Proportion  0.58 1.00
## 
##  With factor correlations of 
##      MR1  MR2
## MR1 1.00 0.21
## MR2 0.21 1.00
## 
## Mean item complexity =  1.3
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  32.41 with Chi Square of  6055.74
## The degrees of freedom for the model are 701  and the objective function was  5.07 
## 
## The root mean square of the residuals (RMSR) is  0.04 
## The df corrected root mean square of the residuals is  0.04 
## 
## The harmonic number of observations is  202 with the empirical chi square  492.2  with prob <  1 
## The total number of observations was  202  with MLE Chi Square =  940.72  with prob <  3.2e-09 
## 
## Tucker Lewis Index of factoring reliability =  0.949
## RMSEA index =  0.048  and the 90 % confidence intervals are  0.034 0.048
## BIC =  -2780.37
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                 MR1  MR2
## Correlation of scores with factors             0.99 0.97
## Multiple R square of scores with factors       0.97 0.95
## Minimum correlation of possible factor scores  0.94 0.90

Factor 1

Study 2, BEETLE condition: Rotated Factor 1

	F1
guilt	0.8818069
embarrassed	0.8485742
emo_recog	0.8484070
disrespected	0.8429130
morality	0.8363959
pride	0.8351696
depressed	0.8279499
love	0.8160320
beliefs	0.7931295
self_restraint	0.7626060
personality	0.7501635
computations	0.7051928
happy	0.7039968
reasoning	0.6839575
joy	0.6837797
thoughts	0.6017860
recognizing	0.5954349
self_aware	0.5830002
angry	0.5825841
nauseated	0.5590958
pleasure	0.5014760
calm	0.4983626
desires	0.4971995
remembering	0.3538826
safe	0.3279109
choices	0.2211951
intentions	0.2136001
fear	0.2032658
free_will	0.1987607
conscious	0.1979713
tired	0.1499592
depth	0.1456539
goal	0.1450279
communicating	0.1153308
pain	-0.0536185
sounds	-0.1192994
odors	-0.1800466
seeing	-0.2176492
temperature	-0.2619471
hungry	-0.4048169

Factor 2

Study 2, BEETLE condition: Rotated Factor 2

	F2
seeing	0.7921610
sounds	0.7790295
odors	0.7360813
temperature	0.7306280
pain	0.7279478
hungry	0.7255994
tired	0.6781598
communicating	0.6780767
choices	0.6542673
fear	0.6490465
goal	0.6286422
intentions	0.6106888
conscious	0.6033525
free_will	0.5704718
safe	0.5488803
depth	0.4919964
calm	0.4875792
remembering	0.4707867
pleasure	0.4612503
desires	0.4264998
thoughts	0.3510397
self_aware	0.3389718
happy	0.3155253
angry	0.2859737
nauseated	0.2794495
joy	0.2776230
recognizing	0.2704992
personality	0.2409035
reasoning	0.1235295
emo_recog	0.0576297
depressed	0.0408385
self_restraint	0.0313338
love	0.0295774
computations	-0.0989659
pride	-0.1426384
beliefs	-0.1602695
disrespected	-0.1641108
morality	-0.1851130
guilt	-0.2156716
embarrassed	-0.2431919

Factor 3 (not applicable)

EFA: ROBOT condition

Step 1: Determine how many factors to extract

Step 2: Run EFA without rotation

## The items do not have an equal number of response alternatives, global set to FALSE

## Factor Analysis using method =  minres
## Call: fa(r = d2_robot, nfactors = nfactors_d2_robot, rotate = "none", 
##     fm = "minres", cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   h2   u2 com
## happy           0.88 -0.05 0.78 0.22 1.0
## depressed       0.88 -0.10 0.78 0.22 1.0
## fear            0.91  0.02 0.83 0.17 1.0
## angry           0.87 -0.03 0.76 0.24 1.0
## calm            0.75  0.15 0.58 0.42 1.1
## sounds         -0.25  0.75 0.63 0.37 1.2
## seeing          0.08  0.80 0.64 0.36 1.0
## temperature    -0.12  0.74 0.57 0.43 1.1
## odors           0.16  0.63 0.43 0.57 1.1
## depth           0.04  0.64 0.41 0.59 1.0
## computations   -0.42  0.69 0.65 0.35 1.7
## thoughts        0.74  0.16 0.58 0.42 1.1
## reasoning       0.38  0.58 0.48 0.52 1.7
## remembering    -0.06  0.79 0.62 0.38 1.0
## beliefs         0.80  0.13 0.66 0.34 1.1
## hungry          0.90 -0.12 0.83 0.17 1.0
## tired           0.85 -0.05 0.73 0.27 1.0
## pain            0.89 -0.10 0.80 0.20 1.0
## nauseated       0.88 -0.11 0.78 0.22 1.0
## safe            0.82  0.05 0.68 0.32 1.0
## love            0.88 -0.07 0.78 0.22 1.0
## recognizing     0.09  0.76 0.58 0.42 1.0
## communicating  -0.03  0.78 0.60 0.40 1.0
## guilt           0.91 -0.05 0.83 0.17 1.0
## disrespected    0.89 -0.05 0.79 0.21 1.0
## free_will       0.73  0.03 0.54 0.46 1.0
## choices         0.16  0.71 0.52 0.48 1.1
## self_restraint  0.63  0.36 0.53 0.47 1.6
## intentions      0.61  0.35 0.49 0.51 1.6
## goal            0.10  0.77 0.61 0.39 1.0
## conscious       0.76  0.12 0.59 0.41 1.0
## self_aware      0.70  0.30 0.58 0.42 1.4
## desires         0.87 -0.02 0.75 0.25 1.0
## embarrassed     0.89 -0.07 0.80 0.20 1.0
## emo_recog       0.69  0.26 0.55 0.45 1.3
## joy             0.88 -0.03 0.78 0.22 1.0
## morality        0.62  0.37 0.52 0.48 1.6
## personality     0.65  0.28 0.51 0.49 1.4
## pleasure        0.91  0.03 0.84 0.16 1.0
## pride           0.89 -0.07 0.79 0.21 1.0
## 
##                         MR1  MR2
## SS loadings           19.14 7.05
## Proportion Var         0.48 0.18
## Cumulative Var         0.48 0.65
## Proportion Explained   0.73 0.27
## Cumulative Proportion  0.73 1.00
## 
## Mean item complexity =  1.1
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  43.28 with Chi Square of  8173.42
## The degrees of freedom for the model are 701  and the objective function was  5.13 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  204 with the empirical chi square  295.44  with prob <  1 
## The total number of observations was  204  with MLE Chi Square =  961.01  with prob <  2e-10 
## 
## Tucker Lewis Index of factoring reliability =  0.961
## RMSEA index =  0.049  and the 90 % confidence intervals are  0.036 0.049
## BIC =  -2767
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                 MR1  MR2
## Correlation of scores with factors             0.99 0.97
## Multiple R square of scores with factors       0.99 0.94
## Minimum correlation of possible factor scores  0.97 0.89

Step 3: Run EFA with oblimin rotation

## The items do not have an equal number of response alternatives, global set to FALSE

## Factor Analysis using method =  minres
## Call: fa(r = d2_robot, nfactors = nfactors_d2_robot, rotate = "oblimin", 
##     fm = "minres", cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   h2   u2 com
## happy           0.88 -0.06 0.78 0.22 1.0
## depressed       0.88 -0.11 0.78 0.22 1.0
## fear            0.91  0.01 0.83 0.17 1.0
## angry           0.87 -0.04 0.76 0.24 1.0
## calm            0.74  0.15 0.58 0.42 1.1
## sounds         -0.26  0.76 0.63 0.37 1.2
## seeing          0.06  0.80 0.64 0.36 1.0
## temperature    -0.13  0.74 0.57 0.43 1.1
## odors           0.15  0.63 0.43 0.57 1.1
## depth           0.03  0.64 0.41 0.59 1.0
## computations   -0.44  0.69 0.65 0.35 1.7
## thoughts        0.74  0.16 0.58 0.42 1.1
## reasoning       0.36  0.58 0.48 0.52 1.7
## remembering    -0.07  0.79 0.62 0.38 1.0
## beliefs         0.80  0.12 0.66 0.34 1.0
## hungry          0.91 -0.13 0.83 0.17 1.0
## tired           0.85 -0.06 0.73 0.27 1.0
## pain            0.89 -0.11 0.80 0.20 1.0
## nauseated       0.88 -0.12 0.78 0.22 1.0
## safe            0.82  0.05 0.68 0.32 1.0
## love            0.88 -0.08 0.78 0.22 1.0
## recognizing     0.08  0.76 0.58 0.42 1.0
## communicating  -0.05  0.78 0.60 0.40 1.0
## guilt           0.91 -0.06 0.83 0.17 1.0
## disrespected    0.89 -0.06 0.79 0.21 1.0
## free_will       0.73  0.02 0.54 0.46 1.0
## choices         0.14  0.71 0.52 0.48 1.1
## self_restraint  0.63  0.35 0.53 0.47 1.6
## intentions      0.60  0.34 0.49 0.51 1.6
## goal            0.08  0.77 0.61 0.39 1.0
## conscious       0.76  0.11 0.59 0.41 1.0
## self_aware      0.70  0.29 0.58 0.42 1.3
## desires         0.87 -0.03 0.75 0.25 1.0
## embarrassed     0.89 -0.08 0.80 0.20 1.0
## emo_recog       0.68  0.26 0.55 0.45 1.3
## joy             0.88 -0.04 0.78 0.22 1.0
## morality        0.61  0.36 0.52 0.48 1.6
## personality     0.65  0.27 0.51 0.49 1.3
## pleasure        0.91  0.02 0.84 0.16 1.0
## pride           0.89 -0.08 0.79 0.21 1.0
## 
##                         MR1  MR2
## SS loadings           19.13 7.06
## Proportion Var         0.48 0.18
## Cumulative Var         0.48 0.65
## Proportion Explained   0.73 0.27
## Cumulative Proportion  0.73 1.00
## 
##  With factor correlations of 
##      MR1  MR2
## MR1 1.00 0.03
## MR2 0.03 1.00
## 
## Mean item complexity =  1.1
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  43.28 with Chi Square of  8173.42
## The degrees of freedom for the model are 701  and the objective function was  5.13 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  204 with the empirical chi square  295.44  with prob <  1 
## The total number of observations was  204  with MLE Chi Square =  961.01  with prob <  2e-10 
## 
## Tucker Lewis Index of factoring reliability =  0.961
## RMSEA index =  0.049  and the 90 % confidence intervals are  0.036 0.049
## BIC =  -2767
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                 MR1  MR2
## Correlation of scores with factors             0.99 0.97
## Multiple R square of scores with factors       0.99 0.94
## Minimum correlation of possible factor scores  0.97 0.89

Factor 1

Study 2, ROBOT condition: Rotated Factor 1

	F1
pleasure	0.9140184
fear	0.9127861
guilt	0.9097826
hungry	0.9074466
embarrassed	0.8924450
disrespected	0.8905751
pride	0.8883128
pain	0.8879718
joy	0.8849706
love	0.8825691
happy	0.8818838
depressed	0.8798968
nauseated	0.8776840
angry	0.8712028
desires	0.8678645
tired	0.8538245
safe	0.8230149
beliefs	0.7975990
conscious	0.7557527
calm	0.7434575
thoughts	0.7403026
free_will	0.7325369
self_aware	0.6960900
emo_recog	0.6846974
personality	0.6485166
self_restraint	0.6264207
morality	0.6091920
intentions	0.6015667
reasoning	0.3639691
odors	0.1464328
choices	0.1416935
goal	0.0833291
recognizing	0.0770145
seeing	0.0591363
depth	0.0283582
communicating	-0.0467481
remembering	-0.0728508
temperature	-0.1331675
sounds	-0.2633899
computations	-0.4372506

Factor 2

Study 2, ROBOT condition: Rotated Factor 2

	F2
seeing	0.7951653
remembering	0.7884925
communicating	0.7766840
goal	0.7730676
recognizing	0.7584561
sounds	0.7566558
temperature	0.7447196
choices	0.7059041
computations	0.6914685
depth	0.6383489
odors	0.6323190
reasoning	0.5787978
morality	0.3618524
self_restraint	0.3545855
intentions	0.3412169
self_aware	0.2918780
personality	0.2714698
emo_recog	0.2573307
thoughts	0.1569122
calm	0.1458297
beliefs	0.1189406
conscious	0.1116294
safe	0.0454009
free_will	0.0208398
pleasure	0.0160182
fear	0.0145319
desires	-0.0273475
angry	-0.0354818
joy	-0.0425873
tired	-0.0594817
guilt	-0.0604850
disrespected	-0.0611247
happy	-0.0632205
love	-0.0758114
pride	-0.0764912
embarrassed	-0.0804950
depressed	-0.1062734
pain	-0.1130480
nauseated	-0.1176668
hungry	-0.1264215

Factor 3 (not applicable)

EFA: ALL conditions

Step 1: Determine how many factors to extract

Step 2: Run EFA without rotation

## The items do not have an equal number of response alternatives, global set to FALSE

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Factor Analysis using method =  minres
## Call: fa(r = d2_all, nfactors = nfactors_d2_all, rotate = "none", fm = "minres", 
##     cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   MR3   h2    u2 com
## happy           0.88 -0.11 -0.13 0.80 0.195 1.1
## depressed       0.84 -0.08 -0.31 0.81 0.185 1.3
## fear            0.81 -0.32  0.28 0.84 0.164 1.6
## angry           0.83 -0.18 -0.04 0.73 0.269 1.1
## calm            0.81 -0.04  0.10 0.67 0.334 1.0
## sounds          0.16  0.64  0.50 0.68 0.315 2.1
## seeing          0.43  0.37  0.63 0.72 0.284 2.4
## temperature     0.24  0.44  0.64 0.66 0.338 2.1
## odors           0.46  0.23  0.60 0.63 0.373 2.2
## depth           0.26  0.57  0.27 0.47 0.531 1.9
## computations   -0.25  0.87 -0.32 0.92 0.078 1.4
## thoughts        0.83 -0.01  0.01 0.68 0.316 1.0
## reasoning       0.44  0.63 -0.20 0.63 0.368 2.0
## remembering     0.17  0.81  0.08 0.69 0.311 1.1
## beliefs         0.69  0.17 -0.41 0.67 0.335 1.8
## hungry          0.64 -0.55  0.48 0.93 0.066 2.9
## tired           0.77 -0.37  0.34 0.84 0.158 1.9
## pain            0.72 -0.45  0.40 0.89 0.106 2.3
## nauseated       0.81 -0.22 -0.03 0.70 0.298 1.1
## safe            0.81 -0.20  0.18 0.73 0.269 1.2
## love            0.82 -0.08 -0.32 0.78 0.216 1.3
## recognizing     0.22  0.81 -0.12 0.72 0.280 1.2
## communicating   0.32  0.64  0.36 0.64 0.356 2.1
## guilt           0.74  0.03 -0.54 0.84 0.158 1.8
## disrespected    0.76 -0.03 -0.46 0.78 0.218 1.6
## free_will       0.73 -0.25  0.31 0.69 0.307 1.6
## choices         0.48  0.52  0.33 0.61 0.391 2.7
## self_restraint  0.66  0.33 -0.25 0.61 0.394 1.8
## intentions      0.72  0.05  0.28 0.60 0.397 1.3
## goal            0.40  0.57  0.36 0.61 0.392 2.6
## conscious       0.76 -0.23  0.28 0.72 0.283 1.5
## self_aware      0.80  0.07  0.00 0.64 0.359 1.0
## desires         0.85 -0.16  0.05 0.75 0.249 1.1
## embarrassed     0.71 -0.01 -0.52 0.77 0.227 1.8
## emo_recog       0.66  0.34 -0.38 0.69 0.308 2.2
## joy             0.87 -0.10 -0.13 0.78 0.219 1.1
## morality        0.53  0.46 -0.43 0.67 0.325 2.9
## personality     0.73  0.29 -0.21 0.65 0.347 1.5
## pleasure        0.85 -0.23  0.10 0.78 0.217 1.2
## pride           0.77 -0.03 -0.45 0.80 0.198 1.6
## 
##                         MR1  MR2  MR3
## SS loadings           17.90 6.23 4.73
## Proportion Var         0.45 0.16 0.12
## Cumulative Var         0.45 0.60 0.72
## Proportion Explained   0.62 0.22 0.16
## Cumulative Proportion  0.62 0.84 1.00
## 
## Mean item complexity =  1.7
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  67.35 with Chi Square of  26324.14
## The degrees of freedom for the model are 663  and the objective function was  26.36 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  406 with the empirical chi square  525.92  with prob <  1 
## The total number of observations was  406  with MLE Chi Square =  10250.64  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.556
## RMSEA index =  0.193  and the 90 % confidence intervals are  0.186 NA
## BIC =  6268.43
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                MR1 MR2 MR3
## Correlation of scores with factors               1   1   1
## Multiple R square of scores with factors         1   1   1
## Minimum correlation of possible factor scores    1   1   1

Step 3: Run EFA with oblimin rotation

## The items do not have an equal number of response alternatives, global set to FALSE

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Factor Analysis using method =  minres
## Call: fa(r = d2_all, nfactors = nfactors_d2_all, rotate = "oblimin", 
##     fm = "minres", cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   MR3   h2    u2 com
## happy           0.70  0.39  0.03 0.80 0.195 1.6
## depressed       0.82  0.23 -0.08 0.81 0.185 1.2
## fear            0.28  0.77  0.13 0.84 0.164 1.3
## angry           0.58  0.48  0.03 0.73 0.269 1.9
## calm            0.47  0.46  0.22 0.67 0.334 2.4
## sounds         -0.21 -0.03  0.85 0.68 0.315 1.1
## seeing         -0.17  0.36  0.79 0.72 0.284 1.5
## temperature    -0.30  0.23  0.81 0.66 0.338 1.4
## odors          -0.14  0.45  0.68 0.63 0.373 1.8
## depth           0.04 -0.10  0.67 0.47 0.531 1.0
## computations    0.21 -0.91  0.40 0.92 0.078 1.5
## thoughts        0.56  0.39  0.18 0.68 0.316 2.0
## reasoning       0.56 -0.36  0.45 0.63 0.368 2.7
## remembering     0.17 -0.42  0.71 0.69 0.311 1.8
## beliefs         0.83 -0.07  0.01 0.67 0.335 1.0
## hungry         -0.04  0.97  0.04 0.93 0.066 1.0
## tired           0.19  0.82  0.12 0.84 0.158 1.2
## pain            0.10  0.90  0.08 0.89 0.106 1.0
## nauseated       0.55  0.49  0.00 0.70 0.298 2.0
## safe            0.38  0.62  0.15 0.73 0.269 1.8
## love            0.82  0.22 -0.08 0.78 0.216 1.2
## recognizing     0.37 -0.53  0.59 0.72 0.280 2.7
## communicating   0.02 -0.06  0.80 0.64 0.356 1.0
## guilt           0.95 -0.03 -0.16 0.84 0.158 1.1
## disrespected    0.89  0.07 -0.15 0.78 0.218 1.1
## free_will       0.21  0.70  0.18 0.69 0.307 1.3
## choices         0.13  0.08  0.72 0.61 0.391 1.1
## self_restraint  0.71 -0.09  0.24 0.61 0.394 1.3
## intentions      0.28  0.48  0.38 0.60 0.397 2.6
## goal            0.06  0.03  0.76 0.61 0.392 1.0
## conscious       0.26  0.69  0.18 0.72 0.283 1.4
## self_aware      0.56  0.31  0.24 0.64 0.359 2.0
## desires         0.52  0.53  0.10 0.75 0.249 2.1
## embarrassed     0.91 -0.01 -0.19 0.77 0.227 1.1
## emo_recog       0.81 -0.18  0.16 0.69 0.308 1.2
## joy             0.69  0.38  0.04 0.78 0.219 1.6
## morality        0.78 -0.35  0.19 0.67 0.325 1.5
## personality     0.71  0.00  0.25 0.65 0.347 1.2
## pleasure        0.47  0.60  0.08 0.78 0.217 1.9
## pride           0.90  0.08 -0.14 0.80 0.198 1.1
## 
##                         MR1  MR2  MR3
## SS loadings           12.67 9.31 6.88
## Proportion Var         0.32 0.23 0.17
## Cumulative Var         0.32 0.55 0.72
## Proportion Explained   0.44 0.32 0.24
## Cumulative Proportion  0.44 0.76 1.00
## 
##  With factor correlations of 
##      MR1  MR2  MR3
## MR1 1.00 0.29 0.25
## MR2 0.29 1.00 0.06
## MR3 0.25 0.06 1.00
## 
## Mean item complexity =  1.5
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  67.35 with Chi Square of  26324.14
## The degrees of freedom for the model are 663  and the objective function was  26.36 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  406 with the empirical chi square  525.92  with prob <  1 
## The total number of observations was  406  with MLE Chi Square =  10250.64  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.556
## RMSEA index =  0.193  and the 90 % confidence intervals are  0.186 NA
## BIC =  6268.43
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                MR1 MR2 MR3
## Correlation of scores with factors               1   1   1
## Multiple R square of scores with factors         1   1   1
## Minimum correlation of possible factor scores    1   1   1

Factor 1

Study 2, ALL conditions: Rotated Factor 1

	F1
guilt	0.9535775
embarrassed	0.9102779
pride	0.8955385
disrespected	0.8886841
beliefs	0.8290025
depressed	0.8228089
love	0.8155435
emo_recog	0.8105082
morality	0.7796098
personality	0.7117920
self_restraint	0.7058779
happy	0.6953173
joy	0.6851919
angry	0.5788629
thoughts	0.5595532
reasoning	0.5576674
self_aware	0.5571677
nauseated	0.5470788
desires	0.5153285
pleasure	0.4693335
calm	0.4681975
safe	0.3793573
recognizing	0.3698177
fear	0.2788078
intentions	0.2765728
conscious	0.2589541
computations	0.2144677
free_will	0.2125231
tired	0.1915450
remembering	0.1706651
choices	0.1309989
pain	0.1011573
goal	0.0622677
depth	0.0407803
communicating	0.0216299
hungry	-0.0371528
odors	-0.1403931
seeing	-0.1715447
sounds	-0.2102279
temperature	-0.2977804

Factor 2

Study 2, ALL conditions: Rotated Factor 2

	F2
hungry	0.9730491
pain	0.8998698
tired	0.8220191
fear	0.7672720
free_will	0.7033836
conscious	0.6883904
safe	0.6225290
pleasure	0.6049713
desires	0.5313655
nauseated	0.4947828
intentions	0.4763306
angry	0.4750855
calm	0.4590066
odors	0.4452891
thoughts	0.3874506
happy	0.3871707
joy	0.3790434
seeing	0.3580389
self_aware	0.3114572
depressed	0.2333356
temperature	0.2303137
love	0.2157570
choices	0.0763286
pride	0.0752228
disrespected	0.0652521
goal	0.0296899
personality	-0.0040902
embarrassed	-0.0111468
sounds	-0.0281385
guilt	-0.0309685
communicating	-0.0583656
beliefs	-0.0683519
self_restraint	-0.0906944
depth	-0.0978803
emo_recog	-0.1781597
morality	-0.3501710
reasoning	-0.3573439
remembering	-0.4176334
recognizing	-0.5265195
computations	-0.9125672

Factor 3

Study 2, ALL conditions: Rotated Factor 3

	F3
sounds	0.8539408
temperature	0.8111799
communicating	0.7988459
seeing	0.7919868
goal	0.7588818
choices	0.7248240
remembering	0.7091640
odors	0.6750699
depth	0.6744605
recognizing	0.5897025
reasoning	0.4508654
computations	0.3982064
intentions	0.3840658
personality	0.2461863
self_aware	0.2385204
self_restraint	0.2362421
calm	0.2180908
morality	0.1907620
thoughts	0.1845226
conscious	0.1829682
free_will	0.1774112
emo_recog	0.1604502
safe	0.1487801
fear	0.1256713
tired	0.1209364
desires	0.1036911
pain	0.0841830
pleasure	0.0805060
hungry	0.0449061
joy	0.0392219
happy	0.0342915
angry	0.0272603
beliefs	0.0148058
nauseated	0.0016504
depressed	-0.0782627
love	-0.0837592
pride	-0.1428292
disrespected	-0.1499834
guilt	-0.1618242
embarrassed	-0.1873396

Confirmatory factor analysis

CFA: All conditions

ModelDD: Data-driven, three factors (experience, MR2, MR3; see Study 1)

## lavaan (0.5-20) converged normally after  69 iterations
## 
##   Number of observations                           406
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             4230.103
##   Degrees of freedom                               737
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            13425.609
##   Degrees of freedom                               780
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.724
##   Tucker-Lewis Index (TLI)                       0.708
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -27438.805
##   Loglikelihood unrestricted model (H1)     -25323.753
## 
##   Number of free parameters                         83
##   Akaike (AIC)                               55043.609
##   Bayesian (BIC)                             55376.136
##   Sample-size adjusted Bayesian (BIC)        55112.766
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.108
##   90 Percent Confidence Interval          0.105  0.111
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.145
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   MR1 =~                                              
##     embarrassed       1.000                           
##     guilt             1.101    0.070   15.767    0.000
##     pride             1.265    0.077   16.366    0.000
##     beliefs           1.030    0.084   12.251    0.000
##     disrespected      1.135    0.075   15.097    0.000
##     love              1.522    0.091   16.700    0.000
##     depressed         1.481    0.085   17.360    0.000
##     emo_recog         1.227    0.096   12.827    0.000
##     morality          0.962    0.104    9.242    0.000
##     personality       1.594    0.116   13.758    0.000
##     joy               1.774    0.103   17.186    0.000
##     happy             1.972    0.111   17.733    0.000
##     self_restraint    1.219    0.117   10.448    0.000
##     thoughts          1.774    0.119   14.951    0.000
##     angry             1.707    0.113   15.146    0.000
##     reasoning         0.988    0.134    7.371    0.000
##     self_aware        1.811    0.128   14.195    0.000
##     nauseated         1.451    0.108   13.488    0.000
##     calm              1.823    0.131   13.958    0.000
##     intentions        1.608    0.145   11.113    0.000
##   MR2 =~                                              
##     hungry            1.000                           
##     pain              0.934    0.040   23.276    0.000
##     tired             0.839    0.036   23.414    0.000
##     fear              0.819    0.036   22.782    0.000
##     pleasure          0.644    0.032   20.128    0.000
##     free_will         0.670    0.038   17.771    0.000
##     safe              0.651    0.035   18.781    0.000
##     conscious         0.721    0.037   19.286    0.000
##     desires           0.589    0.032   18.308    0.000
##   MR3 =~                                              
##     temperature       1.000                           
##     seeing            1.174    0.103   11.444    0.000
##     sounds            1.076    0.091   11.811    0.000
##     depth             1.015    0.101   10.060    0.000
##     remembering       1.229    0.108   11.433    0.000
##     goal              1.270    0.108   11.755    0.000
##     communicating     1.218    0.098   12.389    0.000
##     choices           1.191    0.101   11.795    0.000
##     odors             0.946    0.098    9.667    0.000
##     recognizing       1.106    0.105   10.511    0.000
##     computations      0.740    0.118    6.274    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   MR1 ~~                                              
##     MR2               1.129    0.118    9.563    0.000
##     MR3               0.279    0.052    5.404    0.000
##   MR2 ~~                                              
##     MR3               0.661    0.157    4.204    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     embarrassed       0.420    0.031   13.547    0.000
##     guilt             0.418    0.031   13.395    0.000
##     pride             0.464    0.035   13.231    0.000
##     beliefs           0.901    0.065   13.902    0.000
##     disrespected      0.534    0.039   13.538    0.000
##     love              0.606    0.046   13.121    0.000
##     depressed         0.461    0.036   12.846    0.000
##     emo_recog         1.110    0.080   13.849    0.000
##     morality          1.678    0.119   14.086    0.000
##     personality       1.488    0.108   13.746    0.000
##     joy               0.702    0.054   12.928    0.000
##     happy             0.715    0.057   12.644    0.000
##     self_restraint    1.972    0.141   14.026    0.000
##     thoughts          1.356    0.100   13.565    0.000
##     angry             1.192    0.088   13.529    0.000
##     reasoning         3.021    0.213   14.153    0.000
##     self_aware        1.721    0.126   13.687    0.000
##     nauseated         1.319    0.096   13.779    0.000
##     calm              1.852    0.135   13.720    0.000
##     intentions        2.905    0.208   13.986    0.000
##     hungry            2.139    0.170   12.559    0.000
##     pain              1.348    0.113   11.904    0.000
##     tired             1.057    0.089   11.834    0.000
##     fear              1.147    0.095   12.132    0.000
##     pleasure          1.167    0.090   12.967    0.000
##     free_will         1.898    0.142   13.398    0.000
##     safe              1.509    0.114   13.236    0.000
##     conscious         1.695    0.129   13.144    0.000
##     desires           1.339    0.101   13.316    0.000
##     temperature       2.169    0.165   13.134    0.000
##     seeing            2.295    0.179   12.795    0.000
##     sounds            1.649    0.131   12.547    0.000
##     depth             2.907    0.217   13.393    0.000
##     remembering       2.528    0.198   12.802    0.000
##     goal              2.352    0.187   12.588    0.000
##     communicating     1.606    0.134   12.009    0.000
##     choices           2.035    0.162   12.559    0.000
##     odors             2.906    0.215   13.504    0.000
##     recognizing       2.930    0.221   13.240    0.000
##     computations      5.913    0.422   14.025    0.000
##     MR1               0.490    0.057    8.530    0.000
##     MR2               5.240    0.502   10.436    0.000
##     MR3               1.416    0.210    6.732    0.000

ModelWDM: Theoretical, three factors (AFFECT, AUTONOMY, PERCEPTION; see Weisman et al., 2015)

## lavaan (0.5-20) converged normally after  47 iterations
## 
##   Number of observations                           406
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              574.111
##   Degrees of freedom                               101
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             3556.652
##   Degrees of freedom                               120
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.862
##   Tucker-Lewis Index (TLI)                       0.836
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -11698.470
##   Loglikelihood unrestricted model (H1)     -11411.415
## 
##   Number of free parameters                         35
##   Akaike (AIC)                               23466.941
##   Bayesian (BIC)                             23607.163
##   Sample-size adjusted Bayesian (BIC)        23496.103
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.107
##   90 Percent Confidence Interval          0.099  0.116
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.091
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   affect =~                                           
##     happy             1.000                           
##     depressed         0.656    0.032   20.325    0.000
##     fear              1.056    0.059   17.752    0.000
##     angry             0.861    0.042   20.492    0.000
##     calm              0.956    0.050   19.168    0.000
##     joy               0.908    0.034   26.657    0.000
##   perception =~                                       
##     sounds            1.000                           
##     seeing            1.347    0.117   11.537    0.000
##     temperature       1.194    0.106   11.265    0.000
##     odors             1.296    0.115   11.310    0.000
##     depth             1.048    0.111    9.474    0.000
##   autonomy =~                                         
##     free_will         1.000                           
##     choices           1.023    0.097   10.532    0.000
##     self_restraint    0.601    0.075    8.054    0.000
##     intentions        1.146    0.101   11.308    0.000
##     goal              1.044    0.103   10.156    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   affect ~~                                           
##     perception        0.569    0.106    5.380    0.000
##     autonomy          1.312    0.154    8.527    0.000
##   perception ~~                                       
##     autonomy          1.147    0.148    7.737    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     happy             0.477    0.050    9.587    0.000
##     depressed         0.613    0.048   12.714    0.000
##     fear              2.270    0.172   13.183    0.000
##     angry             1.030    0.081   12.677    0.000
##     calm              1.523    0.118   12.944    0.000
##     joy               0.475    0.046   10.362    0.000
##     sounds            2.009    0.160   12.549    0.000
##     seeing            1.926    0.175   11.003    0.000
##     temperature       1.760    0.154   11.461    0.000
##     odors             2.024    0.178   11.392    0.000
##     depth             2.959    0.228   12.985    0.000
##     free_will         2.644    0.206   12.832    0.000
##     choices           2.367    0.188   12.576    0.000
##     self_restraint    2.123    0.156   13.629    0.000
##     intentions        2.069    0.176   11.776    0.000
##     goal              2.888    0.225   12.834    0.000
##     affect            2.145    0.185   11.617    0.000
##     perception        1.280    0.198    6.469    0.000
##     autonomy          1.602    0.250    6.414    0.000

ModelGGW: Theoretical, two factors (AGENCY, EXPERIENCE; see Gray et al., 2007)

## lavaan (0.5-20) converged normally after  46 iterations
## 
##   Number of observations                           406
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             1736.144
##   Degrees of freedom                               134
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             5043.034
##   Degrees of freedom                               153
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.672
##   Tucker-Lewis Index (TLI)                       0.626
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -12750.702
##   Loglikelihood unrestricted model (H1)     -11882.630
## 
##   Number of free parameters                         37
##   Akaike (AIC)                               25575.404
##   Bayesian (BIC)                             25723.639
##   Sample-size adjusted Bayesian (BIC)        25606.233
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.172
##   90 Percent Confidence Interval          0.164  0.179
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.155
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   experience =~                                       
##     hungry            1.000                           
##     fear              0.909    0.055   16.465    0.000
##     pain              0.972    0.062   15.579    0.000
##     pleasure          0.803    0.047   17.197    0.000
##     angry             0.650    0.041   15.672    0.000
##     desires           0.738    0.045   16.231    0.000
##     personality       0.441    0.043   10.305    0.000
##     conscious         0.799    0.054   14.808    0.000
##     pride             0.341    0.029   11.818    0.000
##     embarrassed       0.244    0.025    9.856    0.000
##     joy               0.614    0.038   15.994    0.000
##   agency =~                                           
##     self_restraint    1.000                           
##     morality          0.905    0.085   10.639    0.000
##     remembering       0.902    0.118    7.642    0.000
##     emo_recog         0.951    0.082   11.588    0.000
##     goal              1.062    0.120    8.842    0.000
##     communicating     0.902    0.107    8.460    0.000
##     thoughts          1.024    0.098   10.400    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   experience ~~                                       
##     agency            1.162    0.159    7.290    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     hungry            3.541    0.267   13.273    0.000
##     fear              1.485    0.121   12.318    0.000
##     pain              2.296    0.179   12.825    0.000
##     pleasure          0.864    0.074   11.659    0.000
##     angry             0.998    0.078   12.782    0.000
##     desires           1.065    0.085   12.475    0.000
##     personality       1.986    0.143   13.911    0.000
##     conscious         1.966    0.150   13.126    0.000
##     pride             0.802    0.058   13.748    0.000
##     embarrassed       0.682    0.049   13.948    0.000
##     joy               0.799    0.063   12.616    0.000
##     self_restraint    1.583    0.131   12.075    0.000
##     morality          1.217    0.102   11.932    0.000
##     remembering       3.759    0.278   13.512    0.000
##     emo_recog         0.836    0.079   10.516    0.000
##     goal              3.374    0.257   13.107    0.000
##     communicating     2.796    0.211   13.256    0.000
##     thoughts          1.725    0.142   12.159    0.000
##     experience        3.838    0.465    8.261    0.000
##     agency            1.119    0.169    6.633    0.000

Compare models (if possible)

# compare models (iff continuous and ML)
customVuong(d2_all_fitDD, d2_all_fitWDM, d2_all_fitGGW)

## $mod1_v_mod2
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 90.678,   p = 2.79e-09
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -82.035,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -82.035,   p = < 2.2e-16
## 
## $mod1_v_mod3
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 65.146,   p = 1.25e-08
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -90.315,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -90.315,   p = < 2.2e-16
## 
## $mod3_v_mod2
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 21.765,   p = 7.04e-09
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -11.194,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -11.194,   p = < 2.2e-16
## 
## $winner
## [1] "WDM"

Study 3 (2016-01-10, 2 conditions, within-subjects)

Demographics

## Warning in mutate_impl(.data, dots): NAs introduced by coercion

Study 3: Exclusion

did_not_finish	failed_catch_trial	did_not_provide_yob	too_young	TOTAL_excluded	TOTAL_participated	OVERALL_TOTAL
13	7	4	0	24	400	424

Study 3: Sample size

condition	n
beetle	200
robot	200
all	200

Study 3: Study duration (minutes)

condition	min_duration	max_duration	median_duration	mean_duration	sd_duration
within-subjects	1.33	36.43	5.46	6.44	3.92

Study 3: Participant age (years; approximate)

condition	min_age	max_age	median_age	mean_age	sd_age
within-subjects	20	68	33	36.84	11.28

Study 3: Participant gender

condition	m	f	other
all	202	198	0

Study 3: Participant race/ethnicity

condition	asian_east	asian_south	black	hispanic	multiracial	white
all	30	4	38	16	22	290

Study 3: Participant religion

condition	buddhism	christianity	islam	none	other	other_prefno
all	10	176	6	190	6	12

Exploratory factor analysis

EFA: ALL conditions

Step 1: Determine how many factors to extract

Step 2: Run EFA without rotation

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Factor Analysis using method =  minres
## Call: fa(r = d3_all, nfactors = nfactors_d3_all, rotate = "none", fm = "minres", 
##     cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   MR3   h2    u2 com
## happy           0.92 -0.05 -0.10 0.85 0.145 1.0
## depressed       0.86  0.00 -0.28 0.82 0.180 1.2
## fear            0.85 -0.36  0.10 0.86 0.142 1.4
## angry           0.88 -0.12 -0.12 0.80 0.196 1.1
## calm            0.87 -0.10  0.05 0.77 0.233 1.0
## sounds          0.36  0.41  0.64 0.71 0.295 2.4
## seeing          0.47  0.15  0.63 0.65 0.352 2.0
## temperature     0.49  0.17  0.67 0.71 0.288 2.0
## odors           0.60 -0.03  0.51 0.62 0.380 2.0
## depth           0.44  0.37  0.44 0.53 0.474 2.9
## computations   -0.42  0.80 -0.18 0.84 0.156 1.6
## thoughts        0.87  0.05  0.00 0.76 0.243 1.0
## reasoning       0.45  0.69 -0.06 0.68 0.321 1.7
## remembering     0.25  0.73  0.21 0.63 0.367 1.4
## beliefs         0.68  0.25 -0.39 0.68 0.324 1.9
## hungry          0.74 -0.58  0.26 0.96 0.042 2.2
## tired           0.83 -0.41  0.12 0.88 0.124 1.5
## pain            0.78 -0.52  0.22 0.92 0.083 1.9
## nauseated       0.85 -0.26 -0.01 0.80 0.202 1.2
## safe            0.82 -0.24  0.10 0.74 0.263 1.2
## love            0.89  0.02 -0.18 0.82 0.180 1.1
## recognizing     0.25  0.79  0.11 0.71 0.295 1.2
## communicating   0.25  0.66  0.25 0.56 0.438 1.6
## guilt           0.80  0.14 -0.39 0.82 0.184 1.5
## disrespected    0.80  0.12 -0.36 0.79 0.213 1.4
## free_will       0.86 -0.22  0.07 0.79 0.214 1.1
## choices         0.60  0.35  0.29 0.56 0.439 2.1
## self_restraint  0.69  0.25 -0.23 0.59 0.406 1.5
## intentions      0.77  0.00  0.17 0.62 0.375 1.1
## goal            0.50  0.44  0.27 0.52 0.484 2.5
## conscious       0.87 -0.21  0.04 0.80 0.199 1.1
## self_aware      0.81  0.00 -0.02 0.65 0.351 1.0
## desires         0.88 -0.23  0.08 0.84 0.161 1.1
## embarrassed     0.78  0.09 -0.45 0.83 0.174 1.6
## emo_recog       0.68  0.43 -0.23 0.70 0.301 1.9
## joy             0.90 -0.05 -0.13 0.83 0.173 1.0
## morality        0.48  0.57 -0.31 0.66 0.340 2.5
## personality     0.75  0.33 -0.14 0.69 0.307 1.4
## pleasure        0.89 -0.24  0.02 0.84 0.156 1.1
## pride           0.82  0.09 -0.37 0.82 0.180 1.4
## 
##                         MR1  MR2  MR3
## SS loadings           20.83 5.43 3.36
## Proportion Var         0.52 0.14 0.08
## Cumulative Var         0.52 0.66 0.74
## Proportion Explained   0.70 0.18 0.11
## Cumulative Proportion  0.70 0.89 1.00
## 
## Mean item complexity =  1.6
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  92.65 with Chi Square of  35656.62
## The degrees of freedom for the model are 663  and the objective function was  47.49 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  400 with the empirical chi square  591.25  with prob <  0.98 
## The total number of observations was  400  with MLE Chi Square =  18180.82  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.406
## RMSEA index =  0.263  and the 90 % confidence intervals are  0.254 NA
## BIC =  14208.48
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                MR1 MR2 MR3
## Correlation of scores with factors               1   1   1
## Multiple R square of scores with factors         1   1   1
## Minimum correlation of possible factor scores    1   1   1

Step 3: Run EFA with oblimin rotation

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Factor Analysis using method =  minres
## Call: fa(r = d3_all, nfactors = nfactors_d3_all, rotate = "oblimin", 
##     fm = "minres", cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR2   MR3   h2    u2 com
## happy           0.77  0.25  0.12 0.85 0.145 1.3
## depressed       0.89  0.12 -0.05 0.82 0.180 1.0
## fear            0.49  0.59  0.17 0.86 0.142 2.1
## angry           0.74  0.30  0.07 0.80 0.196 1.3
## calm            0.60  0.33  0.24 0.77 0.233 1.9
## sounds         -0.18 -0.07  0.91 0.71 0.295 1.1
## seeing         -0.14  0.20  0.82 0.65 0.352 1.2
## temperature    -0.15  0.19  0.86 0.71 0.288 1.2
## odors           0.02  0.36  0.65 0.62 0.380 1.6
## depth           0.04 -0.09  0.71 0.53 0.474 1.0
## computations   -0.01 -0.92  0.06 0.84 0.156 1.0
## thoughts        0.67  0.17  0.25 0.76 0.243 1.4
## reasoning       0.52 -0.56  0.36 0.68 0.321 2.7
## remembering     0.16 -0.55  0.59 0.63 0.367 2.1
## beliefs         0.89 -0.20 -0.10 0.68 0.324 1.1
## hungry          0.23  0.83  0.20 0.96 0.042 1.3
## tired           0.46  0.64  0.16 0.88 0.124 2.0
## pain            0.30  0.76  0.20 0.92 0.083 1.5
## nauseated       0.61  0.46  0.10 0.80 0.202 1.9
## safe            0.49  0.47  0.21 0.74 0.263 2.4
## love            0.83  0.14  0.06 0.82 0.180 1.1
## recognizing     0.25 -0.65  0.52 0.71 0.295 2.2
## communicating   0.11 -0.48  0.60 0.56 0.438 2.0
## guilt           0.96 -0.06 -0.12 0.82 0.184 1.0
## disrespected    0.93 -0.03 -0.09 0.79 0.213 1.0
## free_will       0.55  0.44  0.20 0.79 0.214 2.2
## choices         0.28 -0.08  0.59 0.56 0.439 1.5
## self_restraint  0.76 -0.14  0.07 0.59 0.406 1.1
## intentions      0.45  0.25  0.37 0.62 0.375 2.6
## goal            0.24 -0.19  0.59 0.52 0.484 1.6
## conscious       0.58  0.43  0.18 0.80 0.199 2.1
## self_aware      0.63  0.20  0.19 0.65 0.351 1.4
## desires         0.56  0.47  0.21 0.84 0.161 2.2
## embarrassed     0.99 -0.04 -0.20 0.83 0.174 1.1
## emo_recog       0.79 -0.31  0.14 0.70 0.301 1.4
## joy             0.78  0.24  0.09 0.83 0.173 1.2
## morality        0.73 -0.52  0.07 0.66 0.340 1.8
## personality     0.75 -0.17  0.20 0.69 0.307 1.2
## pleasure        0.61  0.46  0.15 0.84 0.156 2.0
## pride           0.95 -0.01 -0.11 0.82 0.180 1.0
## 
##                         MR1  MR2  MR3
## SS loadings           15.87 7.13 6.62
## Proportion Var         0.40 0.18 0.17
## Cumulative Var         0.40 0.58 0.74
## Proportion Explained   0.54 0.24 0.22
## Cumulative Proportion  0.54 0.78 1.00
## 
##  With factor correlations of 
##      MR1  MR2  MR3
## MR1 1.00 0.26 0.44
## MR2 0.26 1.00 0.12
## MR3 0.44 0.12 1.00
## 
## Mean item complexity =  1.6
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  92.65 with Chi Square of  35656.62
## The degrees of freedom for the model are 663  and the objective function was  47.49 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  400 with the empirical chi square  591.25  with prob <  0.98 
## The total number of observations was  400  with MLE Chi Square =  18180.82  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.406
## RMSEA index =  0.263  and the 90 % confidence intervals are  0.254 NA
## BIC =  14208.48
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                MR1 MR2 MR3
## Correlation of scores with factors               1   1   1
## Multiple R square of scores with factors         1   1   1
## Minimum correlation of possible factor scores    1   1   1

Factor 1

Study 3, ALL conditions: Rotated Factor 1

	F1
embarrassed	0.9887106
guilt	0.9623224
pride	0.9516493
disrespected	0.9318657
beliefs	0.8895247
depressed	0.8869232
love	0.8277407
emo_recog	0.7903127
joy	0.7788934
happy	0.7691707
self_restraint	0.7633349
personality	0.7521296
angry	0.7417027
morality	0.7348283
thoughts	0.6664521
self_aware	0.6275805
pleasure	0.6109389
nauseated	0.6093880
calm	0.5993931
conscious	0.5835354
desires	0.5620457
free_will	0.5528524
reasoning	0.5223481
fear	0.4940615
safe	0.4867439
tired	0.4567330
intentions	0.4450577
pain	0.3039873
choices	0.2819293
recognizing	0.2458594
goal	0.2428450
hungry	0.2334461
remembering	0.1550844
communicating	0.1076928
depth	0.0423794
odors	0.0227834
computations	-0.0132773
seeing	-0.1415658
temperature	-0.1546766
sounds	-0.1800227

Factor 2

Study 3, ALL conditions: Rotated Factor 2

	F2
hungry	0.8280322
pain	0.7594066
tired	0.6370217
fear	0.5852712
safe	0.4717064
desires	0.4654820
nauseated	0.4582278
pleasure	0.4564144
free_will	0.4445940
conscious	0.4299414
odors	0.3569902
calm	0.3283755
angry	0.2977164
intentions	0.2527546
happy	0.2487241
joy	0.2351078
self_aware	0.1987835
seeing	0.1984325
temperature	0.1914984
thoughts	0.1745895
love	0.1449541
depressed	0.1200602
pride	-0.0073606
disrespected	-0.0292760
embarrassed	-0.0376963
guilt	-0.0611414
sounds	-0.0724983
choices	-0.0791271
depth	-0.0885563
self_restraint	-0.1394886
personality	-0.1652057
goal	-0.1929187
beliefs	-0.2005438
emo_recog	-0.3076844
communicating	-0.4806015
morality	-0.5234689
remembering	-0.5490608
reasoning	-0.5560390
recognizing	-0.6483034
computations	-0.9204503

Factor 3

Study 3, ALL conditions: Rotated Factor 3

	F3
sounds	0.9052251
temperature	0.8633502
seeing	0.8165997
depth	0.7117330
odors	0.6492184
communicating	0.5967781
choices	0.5924006
remembering	0.5882180
goal	0.5872050
recognizing	0.5217164
intentions	0.3714754
reasoning	0.3581492
thoughts	0.2534730
calm	0.2371401
safe	0.2133668
desires	0.2112347
pain	0.2008336
hungry	0.1994739
personality	0.1991420
free_will	0.1986224
self_aware	0.1923984
conscious	0.1845408
fear	0.1673922
tired	0.1591889
pleasure	0.1501230
emo_recog	0.1373826
happy	0.1204641
nauseated	0.0989030
joy	0.0856734
morality	0.0720772
angry	0.0662490
self_restraint	0.0662464
love	0.0639495
computations	0.0611026
depressed	-0.0469676
disrespected	-0.0949855
beliefs	-0.1016768
pride	-0.1131357
guilt	-0.1176527
embarrassed	-0.2046707

Confirmatory factor analysis

CFA: All conditions

ModelDD: Data-driven, three factors (MR1, MR2, MR3; see Study 1)

## lavaan (0.5-20) converged normally after  71 iterations
## 
##   Number of observations                           400
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             3764.517
##   Degrees of freedom                               737
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            13689.925
##   Degrees of freedom                               780
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.765
##   Tucker-Lewis Index (TLI)                       0.752
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -28661.020
##   Loglikelihood unrestricted model (H1)     -26778.761
## 
##   Number of free parameters                         83
##   Akaike (AIC)                               57488.040
##   Bayesian (BIC)                             57819.331
##   Sample-size adjusted Bayesian (BIC)        57555.967
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.101
##   90 Percent Confidence Interval          0.098  0.105
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.129
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   MR1 =~                                              
##     embarrassed       1.000                           
##     guilt             1.041    0.073   14.326    0.000
##     pride             1.344    0.090   14.965    0.000
##     beliefs           0.950    0.081   11.730    0.000
##     disrespected      1.079    0.076   14.266    0.000
##     love              1.613    0.099   16.261    0.000
##     depressed         1.310    0.083   15.788    0.000
##     emo_recog         1.187    0.097   12.184    0.000
##     morality          0.849    0.100    8.499    0.000
##     personality       1.525    0.111   13.684    0.000
##     joy               1.810    0.106   17.034    0.000
##     happy             1.848    0.108   17.182    0.000
##     self_restraint    1.316    0.109   12.106    0.000
##     thoughts          1.857    0.120   15.486    0.000
##     angry             1.803    0.112   16.098    0.000
##     reasoning         0.915    0.118    7.782    0.000
##     self_aware        1.664    0.120   13.875    0.000
##     nauseated         1.663    0.112   14.884    0.000
##     calm              1.865    0.123   15.194    0.000
##     intentions        1.575    0.128   12.274    0.000
##   MR2 =~                                              
##     hungry            1.000                           
##     pain              0.946    0.043   21.809    0.000
##     tired             0.931    0.041   22.820    0.000
##     fear              0.904    0.040   22.733    0.000
##     pleasure          0.798    0.036   22.144    0.000
##     free_will         0.821    0.041   20.210    0.000
##     safe              0.777    0.040   19.440    0.000
##     conscious         0.862    0.042   20.711    0.000
##     desires           0.817    0.036   22.660    0.000
##   MR3 =~                                              
##     temperature       1.000                           
##     seeing            0.864    0.077   11.193    0.000
##     sounds            0.825    0.068   12.084    0.000
##     depth             0.959    0.083   11.602    0.000
##     remembering       0.857    0.083   10.366    0.000
##     goal              0.971    0.088   11.082    0.000
##     communicating     0.787    0.080    9.816    0.000
##     choices           0.947    0.084   11.342    0.000
##     odors             0.959    0.090   10.687    0.000
##     recognizing       0.828    0.085    9.730    0.000
##     computations     -0.034    0.105   -0.322    0.747
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   MR1 ~~                                              
##     MR2               1.719    0.172    9.986    0.000
##     MR3               0.618    0.088    7.053    0.000
##   MR2 ~~                                              
##     MR3               1.411    0.209    6.758    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     embarrassed       0.828    0.061   13.667    0.000
##     guilt             0.760    0.056   13.580    0.000
##     pride             1.034    0.077   13.454    0.000
##     beliefs           1.311    0.095   13.872    0.000
##     disrespected      0.831    0.061   13.590    0.000
##     love              0.929    0.071   13.039    0.000
##     depressed         0.738    0.056   13.225    0.000
##     emo_recog         1.812    0.131   13.836    0.000
##     morality          2.538    0.181   14.031    0.000
##     personality       1.970    0.144   13.678    0.000
##     joy               0.824    0.065   12.573    0.000
##     happy             0.795    0.064   12.447    0.000
##     self_restraint    2.276    0.164   13.843    0.000
##     thoughts          1.653    0.124   13.320    0.000
##     angry             1.240    0.095   13.109    0.000
##     reasoning         3.654    0.260   14.052    0.000
##     self_aware        2.220    0.163   13.651    0.000
##     nauseated         1.624    0.121   13.472    0.000
##     calm              1.844    0.138   13.399    0.000
##     intentions        3.114    0.225   13.829    0.000
##     hungry            2.275    0.178   12.815    0.000
##     pain              1.805    0.143   12.643    0.000
##     tired             1.421    0.116   12.297    0.000
##     fear              1.366    0.111   12.330    0.000
##     pleasure          1.202    0.096   12.539    0.000
##     free_will         1.841    0.141   13.037    0.000
##     safe              1.894    0.144   13.181    0.000
##     conscious         1.851    0.143   12.929    0.000
##     desires           1.132    0.092   12.358    0.000
##     temperature       2.097    0.172   12.168    0.000
##     seeing            2.243    0.176   12.768    0.000
##     sounds            1.527    0.124   12.298    0.000
##     depth             2.427    0.193   12.573    0.000
##     remembering       2.857    0.218   13.082    0.000
##     goal              2.935    0.229   12.816    0.000
##     communicating     2.852    0.215   13.247    0.000
##     choices           2.573    0.203   12.700    0.000
##     odors             3.242    0.250   12.970    0.000
##     recognizing       3.241    0.244   13.270    0.000
##     computations      7.374    0.521   14.141    0.000
##     MR1               0.813    0.101    8.019    0.000
##     MR2               5.356    0.520   10.289    0.000
##     MR3               1.914    0.257    7.440    0.000

ModelWDM: Theoretical, three factors (AFFECT, AUTONOMY, PERCEPTION; see Weisman et al., 2015)

## lavaan (0.5-20) converged normally after  50 iterations
## 
##   Number of observations                           400
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              391.505
##   Degrees of freedom                               101
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             3807.455
##   Degrees of freedom                               120
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.921
##   Tucker-Lewis Index (TLI)                       0.906
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -11842.660
##   Loglikelihood unrestricted model (H1)     -11646.907
## 
##   Number of free parameters                         35
##   Akaike (AIC)                               23755.320
##   Bayesian (BIC)                             23895.021
##   Sample-size adjusted Bayesian (BIC)        23783.964
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.085
##   90 Percent Confidence Interval          0.076  0.094
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.069
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   affect =~                                           
##     happy             1.000                           
##     depressed         0.652    0.033   19.860    0.000
##     fear              1.101    0.053   20.924    0.000
##     angry             0.970    0.040   24.032    0.000
##     calm              1.017    0.046   21.902    0.000
##     joy               0.972    0.036   27.273    0.000
##   perception =~                                       
##     sounds            1.000                           
##     seeing            1.109    0.096   11.575    0.000
##     temperature       1.295    0.102   12.650    0.000
##     odors             1.333    0.112   11.865    0.000
##     depth             1.083    0.101   10.701    0.000
##   autonomy =~                                         
##     free_will         1.000                           
##     choices           0.666    0.055   12.057    0.000
##     self_restraint    0.616    0.051   12.027    0.000
##     intentions        0.913    0.058   15.710    0.000
##     goal              0.574    0.059    9.665    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   affect ~~                                           
##     perception        0.906    0.133    6.832    0.000
##     autonomy          2.727    0.250   10.891    0.000
##   perception ~~                                       
##     autonomy          1.395    0.173    8.058    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     happy             0.647    0.063   10.310    0.000
##     depressed         0.891    0.069   12.976    0.000
##     fear              2.203    0.172   12.795    0.000
##     angry             1.131    0.094   12.094    0.000
##     calm              1.649    0.131   12.606    0.000
##     joy               0.723    0.066   10.899    0.000
##     sounds            1.477    0.128   11.542    0.000
##     seeing            2.007    0.170   11.795    0.000
##     temperature       1.742    0.167   10.433    0.000
##     odors             2.598    0.226   11.515    0.000
##     depth             2.604    0.210   12.426    0.000
##     free_will         1.974    0.185   10.656    0.000
##     choices           2.747    0.210   13.089    0.000
##     self_restraint    2.365    0.181   13.097    0.000
##     intentions        2.228    0.192   11.621    0.000
##     goal              3.593    0.265   13.550    0.000
##     affect            2.926    0.252   11.603    0.000
##     perception        1.352    0.186    7.272    0.000
##     autonomy          3.479    0.379    9.167    0.000

ModelGGW: Theoretical, two factors (AGENCY, EXPERIENCE; see Gray et al., 2007)

## lavaan (0.5-20) converged normally after  46 iterations
## 
##   Number of observations                           400
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             1456.993
##   Degrees of freedom                               134
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             5368.619
##   Degrees of freedom                               153
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.746
##   Tucker-Lewis Index (TLI)                       0.710
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -13320.986
##   Loglikelihood unrestricted model (H1)     -12592.489
## 
##   Number of free parameters                         37
##   Akaike (AIC)                               26715.972
##   Bayesian (BIC)                             26863.656
##   Sample-size adjusted Bayesian (BIC)        26746.253
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.157
##   90 Percent Confidence Interval          0.150  0.164
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.131
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   experience =~                                       
##     hungry            1.000                           
##     fear              0.990    0.056   17.669    0.000
##     pain              0.969    0.061   15.954    0.000
##     pleasure          0.927    0.050   18.567    0.000
##     angry             0.793    0.046   17.154    0.000
##     desires           0.931    0.050   18.465    0.000
##     personality       0.565    0.048   11.890    0.000
##     conscious         0.974    0.057   17.198    0.000
##     pride             0.490    0.038   12.870    0.000
##     embarrassed       0.360    0.031   11.591    0.000
##     joy               0.760    0.044   17.375    0.000
##   agency =~                                           
##     self_restraint    1.000                           
##     morality          0.750    0.078    9.623    0.000
##     remembering       0.620    0.089    6.980    0.000
##     emo_recog         0.929    0.078   11.858    0.000
##     goal              0.855    0.095    8.970    0.000
##     communicating     0.581    0.086    6.727    0.000
##     thoughts          1.266    0.099   12.835    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   experience ~~                                       
##     agency            1.984    0.229    8.655    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     hungry            3.432    0.258   13.328    0.000
##     fear              1.631    0.131   12.455    0.000
##     pain              2.657    0.202   13.154    0.000
##     pleasure          1.009    0.086   11.750    0.000
##     angry             1.244    0.098   12.725    0.000
##     desires           1.064    0.090   11.852    0.000
##     personality       2.519    0.183   13.788    0.000
##     conscious         1.850    0.146   12.705    0.000
##     pride             1.494    0.109   13.693    0.000
##     embarrassed       1.098    0.079   13.813    0.000
##     joy               1.062    0.084   12.618    0.000
##     self_restraint    2.011    0.168   11.985    0.000
##     morality          2.182    0.167   13.033    0.000
##     remembering       3.618    0.264   13.688    0.000
##     emo_recog         1.512    0.130   11.658    0.000
##     goal              3.514    0.265   13.249    0.000
##     communicating     3.472    0.253   13.727    0.000
##     thoughts          1.778    0.174   10.210    0.000
##     experience        4.199    0.490    8.576    0.000
##     agency            1.673    0.236    7.096    0.000

Compare models (if possible)

# compare models (iff continuous and ML)
customVuong(d3_all_fitDD, d3_all_fitWDM, d3_all_fitGGW)

## $mod1_v_mod2
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 93.741,   p = 6e-09
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -86.854,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -86.854,   p = < 2.2e-16
## 
## $mod1_v_mod3
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 59.821,   p = <2e-16
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -99.167,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -99.167,   p = < 2.2e-16
## 
## $mod3_v_mod2
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 27.619,   p = 3.18e-08
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -14.065,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -14.065,   p = < 2.2e-16
## 
## $winner
## [1] "WDM"

Study 4 (2016-01-14, 21 conditions, between-subjects)

Demographics

Study 4: Exclusion

did_not_finish	failed_catch_trial	did_not_provide_yob	too_young	TOTAL_excluded	TOTAL_participated	OVERALL_TOTAL
15	24	1	0	40	431	471

Study 4: Sample size

condition	n
adult	21
bear	20
beetle	19
bluejay	20
car	23
child	20
chimpanzee	21
computer	22
dog	24
dolphin	22
elephant	21
fetus	20
fish	20
frog	21
goat	20
infant	19
microbe	20
mouse	18
pvs	21
robot	22
stapler	17
all	431

Study 4: Study duration (minutes)

condition	min_duration	max_duration	median_duration	mean_duration	sd_duration
adult	1.20	41.08	2.57	6.99	11.38
bear	1.65	8.07	3.53	3.84	1.78
beetle	1.40	4.70	2.78	2.82	0.92
bluejay	1.68	12.95	3.50	4.21	2.78
car	0.62	28.50	2.22	3.47	5.57
child	1.57	7.02	3.15	3.56	1.45
chimpanzee	2.08	5.88	3.48	3.61	1.31
computer	1.30	21.77	2.75	4.33	4.39
dog	1.80	7.97	2.79	3.11	1.59
dolphin	0.70	11.18	2.96	3.93	2.42
elephant	1.27	5.08	2.47	2.87	1.04
fetus	1.42	12.33	2.72	3.40	2.35
fish	1.35	7.97	3.37	3.40	1.65
frog	1.80	32.23	3.52	6.31	6.80
goat	1.63	9.17	3.38	4.20	2.57
infant	1.78	45.18	4.05	6.06	9.65
microbe	1.02	42.28	2.73	4.69	8.92
mouse	1.50	7.92	3.40	3.78	1.76
pvs	1.13	7.58	2.22	2.72	1.54
robot	1.72	22.15	3.38	4.43	4.24
stapler	1.17	13.17	1.67	2.92	2.86
all	0.62	45.18	2.88	4.03	4.76

## Joining by: c("condition", "min_age", "max_age", "median_age", "mean_age", "sd_age")

## Warning: joining character vector and factor, coercing into character
## vector

Study 4: Participant age (years; approximate)

condition	min_age	max_age	median_age	mean_age	sd_age
adult	22	55	30.0	30.86	7.83
bear	20	64	35.5	35.75	11.74
beetle	21	45	30.0	30.37	5.22
bluejay	24	60	35.0	38.20	11.00
car	21	55	34.0	33.96	9.47
child	22	68	33.5	36.25	12.13
chimpanzee	22	57	35.0	36.48	10.88
computer	23	59	34.0	35.14	11.15
dog	19	61	30.5	33.42	11.10
dolphin	24	65	33.5	37.82	11.74
elephant	22	66	34.0	40.24	13.51
fetus	21	70	31.0	34.30	10.85
fish	21	66	33.5	36.65	12.77
frog	24	60	34.0	36.86	9.66
goat	18	64	30.0	34.90	12.93
infant	22	54	32.0	34.42	9.11
microbe	20	58	32.5	37.75	12.37
mouse	21	59	40.5	39.89	11.93
pvs	24	65	34.0	35.24	9.59
robot	23	59	40.5	41.91	11.27
stapler	22	70	34.0	36.41	12.08
all	18	70	34.0	36.03	11.11

Study 4: Participant gender

condition	m	f	other
adult	16	5	0
bear	9	11	0
beetle	11	8	0
bluejay	5	15	0
car	12	11	0
child	10	9	1
chimpanzee	13	8	0
computer	11	11	0
dog	14	10	0
dolphin	12	10	0
elephant	7	14	0
fetus	13	7	0
fish	9	11	0
frog	12	9	0
goat	9	11	0
infant	12	6	1
microbe	11	9	0
mouse	8	9	1
pvs	11	10	0
robot	8	14	0
stapler	10	7	0
all	223	205	3

Study 4: Participant race/ethnicity

condition	asian_east	asian_other	asian_south	black	hispanic	middle_eastern	multiracial	native_american	other_prefno	white
adult	1	1	0	4	0	1	0	0	0	14
bear	1	1	0	1	0	0	0	1	0	16
beetle	0	0	0	1	2	0	0	0	0	16
bluejay	0	0	1	3	0	0	1	0	0	15
car	2	0	1	0	2	0	1	0	0	17
child	2	0	0	0	0	0	0	0	1	17
chimpanzee	1	0	0	1	1	0	0	0	0	18
computer	0	0	0	2	0	0	2	0	0	18
dog	2	0	0	2	1	0	0	0	0	19
dolphin	2	1	0	0	1	0	2	0	0	16
elephant	0	1	0	0	1	0	2	0	0	17
fetus	1	0	0	0	4	0	2	0	0	13
fish	2	0	0	3	1	0	0	0	0	14
frog	2	0	0	1	3	0	0	0	0	15
goat	1	0	0	3	1	0	1	0	0	14
infant	1	0	0	2	0	0	1	0	1	14
microbe	2	0	0	1	0	0	3	0	1	13
mouse	2	0	0	0	0	0	0	0	0	16
pvs	2	0	0	1	1	0	0	0	0	17
robot	1	0	0	1	2	0	0	0	0	18
stapler	1	0	2	0	0	0	1	0	0	13
all	26	4	4	26	20	1	16	1	3	330

Study 4: Participant education

condition	some_HS	HS_diploma	some_college	associates	bachelors	some_grad	grad	pref_no
adult	0	1	5	0	7	3	5	0
bear	1	1	7	7	3	1	0	0
beetle	0	3	3	4	6	1	2	0
bluejay	0	2	3	2	9	2	2	0
car	1	0	7	4	7	1	3	0
child	0	1	6	1	7	1	3	1
chimpanzee	0	1	12	0	5	0	2	1
computer	0	2	6	2	9	1	2	0
dog	0	3	5	1	10	1	4	0
dolphin	0	4	4	3	6	3	2	0
elephant	0	2	5	3	7	0	4	0
fetus	0	2	9	4	4	1	0	0
fish	0	3	5	1	6	3	2	0
frog	0	2	7	1	7	1	3	0
goat	1	3	5	5	5	0	1	0
infant	0	2	2	2	8	0	3	2
microbe	0	4	3	2	9	1	1	0
mouse	0	1	5	2	7	0	3	0
pvs	0	1	4	3	9	2	1	1
robot	0	3	3	2	10	1	3	0
stapler	0	0	5	2	5	0	5	0
all	3	41	111	51	146	23	51	5

Exploratory factor analysis

EFA: ALL conditions

Step 1: Determine how many factors to extract

Step 2: Run EFA without rotation

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Factor Analysis using method =  minres
## Call: fa(r = d4_all, nfactors = nfactors_d4_all, rotate = "none", fm = "minres", 
##     cor = "poly")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                 MR1   MR2   MR3   h2    u2 com
## happy          0.91 -0.08 -0.24 0.89 0.107 1.2
## depressed      0.88  0.09 -0.16 0.82 0.182 1.1
## fear           0.88 -0.36 -0.08 0.91 0.094 1.4
## angry          0.90 -0.09 -0.12 0.83 0.170 1.1
## calm           0.89 -0.19 -0.13 0.84 0.160 1.1
## sounds         0.78 -0.32  0.42 0.88 0.118 1.9
## seeing         0.84 -0.29  0.28 0.88 0.121 1.5
## temperature    0.71 -0.31  0.48 0.83 0.174 2.2
## odors          0.84 -0.24  0.19 0.80 0.200 1.3
## depth          0.77  0.03  0.41 0.75 0.246 1.5
## computations   0.29  0.78  0.44 0.89 0.114 1.9
## thoughts       0.88 -0.01 -0.10 0.79 0.207 1.0
## reasoning      0.80  0.36  0.19 0.80 0.201 1.5
## remembering    0.79  0.15  0.40 0.81 0.189 1.6
## beliefs        0.76  0.50 -0.19 0.87 0.128 1.9
## hungry         0.86 -0.45 -0.14 0.96 0.040 1.6
## tired          0.89 -0.36 -0.10 0.94 0.063 1.3
## pain           0.88 -0.41 -0.14 0.96 0.043 1.5
## nauseated      0.87 -0.17 -0.15 0.81 0.193 1.1
## safe           0.88 -0.21 -0.08 0.83 0.168 1.1
## love           0.88  0.01 -0.26 0.85 0.153 1.2
## recognizing    0.83  0.01  0.19 0.72 0.276 1.1
## communicating  0.79 -0.04  0.39 0.78 0.216 1.5
## guilt          0.84  0.37 -0.24 0.90 0.101 1.6
## disrespected   0.83  0.35 -0.17 0.84 0.156 1.4
## free_will      0.86 -0.06 -0.03 0.74 0.257 1.0
## choices        0.83  0.01  0.32 0.79 0.205 1.3
## self_restraint 0.82  0.35  0.07 0.80 0.195 1.4
## intentions     0.86  0.05  0.04 0.74 0.257 1.0
## goal           0.73  0.15  0.34 0.67 0.328 1.5
## conscious      0.86 -0.16 -0.04 0.78 0.224 1.1
## self_aware     0.82  0.22 -0.02 0.71 0.286 1.1
## desires        0.91 -0.11 -0.09 0.85 0.153 1.1
## embarrassed    0.81  0.41 -0.28 0.90 0.099 1.8
## emo_recog      0.83  0.30 -0.04 0.79 0.213 1.3
## joy            0.92 -0.07 -0.20 0.90 0.099 1.1
## morality       0.78  0.48 -0.06 0.84 0.158 1.7
## personality    0.92  0.00 -0.12 0.86 0.140 1.0
## pleasure       0.93 -0.20 -0.11 0.91 0.088 1.1
## pride          0.88  0.24 -0.18 0.87 0.131 1.2
## 
##                         MR1  MR2  MR3
## SS loadings           28.05 3.21 2.09
## Proportion Var         0.70 0.08 0.05
## Cumulative Var         0.70 0.78 0.83
## Proportion Explained   0.84 0.10 0.06
## Cumulative Proportion  0.84 0.94 1.00
## 
## Mean item complexity =  1.4
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  110.45 with Chi Square of  45928.21
## The degrees of freedom for the model are 663  and the objective function was  48.75 
## 
## The root mean square of the residuals (RMSR) is  0.02 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  431 with the empirical chi square  395.68  with prob <  1 
## The total number of observations was  431  with MLE Chi Square =  20176.3  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.489
## RMSEA index =  0.267  and the 90 % confidence intervals are  0.258 NA
## BIC =  16154.47
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                MR1 MR2 MR3
## Correlation of scores with factors               1   1   1
## Multiple R square of scores with factors         1   1   1
## Minimum correlation of possible factor scores    1   1   1

Step 3: Run EFA with oblimin rotation

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate =
## rotate, : A Heywood case was detected. Examine the loadings carefully.

## Factor Analysis using method =  minres
## Call: fa(r = d4_all, nfactors = nfactors_d4_all, rotate = "oblimin", 
##     fm = "minres", cor = "poly")
## 
##  Warning: A Heywood case was detected. 
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  MR1   MR3   MR2   h2    u2 com
## happy           0.78  0.10  0.31 0.89 0.107 1.3
## depressed       0.80  0.11  0.11 0.82 0.182 1.1
## fear            0.40  0.42  0.44 0.91 0.094 3.0
## angry           0.65  0.25  0.24 0.83 0.170 1.6
## calm            0.58  0.28  0.33 0.84 0.160 2.1
## sounds         -0.13  0.99  0.09 0.88 0.118 1.1
## seeing          0.07  0.83  0.16 0.88 0.121 1.1
## temperature    -0.23  1.03  0.05 0.83 0.174 1.1
## odors           0.20  0.68  0.18 0.80 0.200 1.3
## depth           0.11  0.82 -0.19 0.75 0.246 1.1
## computations    0.28  0.33 -0.89 0.89 0.114 1.5
## thoughts        0.67  0.23  0.16 0.79 0.207 1.4
## reasoning       0.57  0.41 -0.33 0.80 0.201 2.5
## remembering     0.22  0.76 -0.28 0.81 0.189 1.5
## beliefs         1.03 -0.16 -0.22 0.87 0.128 1.1
## hungry          0.39  0.37  0.56 0.96 0.040 2.6
## tired           0.43  0.40  0.46 0.94 0.063 3.0
## pain            0.43  0.37  0.52 0.96 0.043 2.8
## nauseated       0.60  0.24  0.32 0.81 0.193 1.9
## safe            0.51  0.35  0.32 0.83 0.168 2.5
## love            0.84  0.03  0.24 0.85 0.153 1.2
## recognizing     0.36  0.57 -0.03 0.72 0.276 1.7
## communicating   0.10  0.84 -0.12 0.78 0.216 1.1
## guilt           1.03 -0.12 -0.08 0.90 0.101 1.0
## disrespected    0.95 -0.03 -0.10 0.84 0.156 1.0
## free_will       0.55  0.34  0.15 0.74 0.257 1.9
## choices         0.23  0.74 -0.11 0.79 0.205 1.2
## self_restraint  0.71  0.27 -0.24 0.80 0.195 1.5
## intentions      0.55  0.38  0.03 0.74 0.257 1.8
## goal            0.24  0.66 -0.26 0.67 0.328 1.6
## conscious       0.49  0.37  0.25 0.78 0.224 2.4
## self_aware      0.70  0.21 -0.09 0.71 0.286 1.2
## desires         0.61  0.30  0.25 0.85 0.153 1.8
## embarrassed     1.08 -0.21 -0.08 0.90 0.099 1.1
## emo_recog       0.79  0.15 -0.14 0.79 0.213 1.1
## joy             0.76  0.15  0.28 0.90 0.099 1.3
## morality        0.89  0.03 -0.29 0.84 0.158 1.2
## personality     0.71  0.23  0.17 0.86 0.140 1.3
## pleasure        0.58  0.32  0.34 0.91 0.088 2.2
## pride           0.92  0.02  0.01 0.87 0.131 1.0
## 
##                         MR1   MR3  MR2
## SS loadings           18.15 11.47 3.72
## Proportion Var         0.45  0.29 0.09
## Cumulative Var         0.45  0.74 0.83
## Proportion Explained   0.54  0.34 0.11
## Cumulative Proportion  0.54  0.89 1.00
## 
##  With factor correlations of 
##      MR1  MR3  MR2
## MR1 1.00 0.68 0.13
## MR3 0.68 1.00 0.26
## MR2 0.13 0.26 1.00
## 
## Mean item complexity =  1.6
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  780  and the objective function was  110.45 with Chi Square of  45928.21
## The degrees of freedom for the model are 663  and the objective function was  48.75 
## 
## The root mean square of the residuals (RMSR) is  0.02 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  431 with the empirical chi square  395.68  with prob <  1 
## The total number of observations was  431  with MLE Chi Square =  20176.3  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.489
## RMSEA index =  0.267  and the 90 % confidence intervals are  0.258 NA
## BIC =  16154.47
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                MR1 MR3 MR2
## Correlation of scores with factors               1   1   1
## Multiple R square of scores with factors         1   1   1
## Minimum correlation of possible factor scores    1   1   1

Factor 1

Study 4, ALL conditions: Rotated Factor 1

	F1
embarrassed	1.0820716
guilt	1.0309219
beliefs	1.0283961
disrespected	0.9476156
pride	0.9156754
morality	0.8924877
love	0.8382325
depressed	0.7991122
emo_recog	0.7880119
happy	0.7773658
joy	0.7584880
personality	0.7136321
self_restraint	0.7053528
self_aware	0.7016795
thoughts	0.6712255
angry	0.6482751
desires	0.6103721
nauseated	0.6021750
pleasure	0.5786861
calm	0.5774913
reasoning	0.5679234
intentions	0.5516153
free_will	0.5487244
safe	0.5139326
conscious	0.4916117
tired	0.4343427
pain	0.4293049
fear	0.3971371
hungry	0.3898447
recognizing	0.3593701
computations	0.2845603
goal	0.2445056
choices	0.2253831
remembering	0.2217424
odors	0.2039732
depth	0.1125124
communicating	0.0999231
seeing	0.0727370
sounds	-0.1274467
temperature	-0.2257676

Factor 2

Study 4, ALL conditions: Rotated Factor 2

	F2
temperature	1.0322391
sounds	0.9910308
communicating	0.8377954
seeing	0.8307419
depth	0.8168775
remembering	0.7626609
choices	0.7444741
odors	0.6830421
goal	0.6581319
recognizing	0.5718535
fear	0.4237692
reasoning	0.4116967
tired	0.3990812
intentions	0.3794416
conscious	0.3733057
hungry	0.3719424
pain	0.3653555
safe	0.3518118
free_will	0.3402245
computations	0.3271320
pleasure	0.3234974
desires	0.2993465
calm	0.2793205
self_restraint	0.2663888
angry	0.2480754
nauseated	0.2386242
thoughts	0.2348611
personality	0.2273632
self_aware	0.2060758
emo_recog	0.1519616
joy	0.1484148
depressed	0.1136922
happy	0.1024259
morality	0.0267690
love	0.0254947
pride	0.0230644
disrespected	-0.0333904
guilt	-0.1208072
beliefs	-0.1578255
embarrassed	-0.2090879

Factor 3

Study 4, ALL conditions: Rotated Factor 3

	F3
hungry	0.5567816
pain	0.5198010
tired	0.4565798
fear	0.4439222
pleasure	0.3357269
calm	0.3344265
nauseated	0.3219476
safe	0.3161502
happy	0.3053946
joy	0.2760150
conscious	0.2548625
desires	0.2456420
love	0.2444304
angry	0.2426271
odors	0.1761402
personality	0.1689421
seeing	0.1641609
thoughts	0.1613108
free_will	0.1549054
depressed	0.1146631
sounds	0.0944280
temperature	0.0478709
intentions	0.0305126
pride	0.0068753
recognizing	-0.0292999
guilt	-0.0789401
embarrassed	-0.0841611
self_aware	-0.0851286
disrespected	-0.0981185
choices	-0.1141279
communicating	-0.1218180
emo_recog	-0.1416160
depth	-0.1863317
beliefs	-0.2221113
self_restraint	-0.2424921
goal	-0.2553232
remembering	-0.2801699
morality	-0.2855495
reasoning	-0.3291966
computations	-0.8875047

Confirmatory factor analysis

CFA: ALL conditions

ModelDD: Data-driven, three factors (MR1, MR2, MR3; see Study 1)

## lavaan (0.5-20) converged normally after  60 iterations
## 
##   Number of observations                           431
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             5096.451
##   Degrees of freedom                               737
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            22441.501
##   Degrees of freedom                               780
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.799
##   Tucker-Lewis Index (TLI)                       0.787
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -29668.644
##   Loglikelihood unrestricted model (H1)     -27120.419
## 
##   Number of free parameters                         83
##   Akaike (AIC)                               59503.288
##   Bayesian (BIC)                             59840.775
##   Sample-size adjusted Bayesian (BIC)        59577.381
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.117
##   90 Percent Confidence Interval          0.114  0.120
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.089
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   MR1 =~                                              
##     embarrassed       1.000                           
##     guilt             1.041    0.057   18.162    0.000
##     pride             1.203    0.061   19.711    0.000
##     beliefs           0.890    0.056   16.013    0.000
##     disrespected      1.022    0.059   17.464    0.000
##     love              1.357    0.066   20.644    0.000
##     depressed         1.280    0.066   19.401    0.000
##     emo_recog         1.038    0.057   18.303    0.000
##     morality          0.939    0.057   16.414    0.000
##     personality       1.410    0.067   21.193    0.000
##     joy               1.476    0.069   21.446    0.000
##     happy             1.452    0.069   21.140    0.000
##     self_restraint    0.987    0.058   16.929    0.000
##     thoughts          1.285    0.066   19.399    0.000
##     angry             1.397    0.070   20.045    0.000
##     reasoning         0.985    0.062   15.983    0.000
##     self_aware        1.089    0.063   17.321    0.000
##     nauseated         1.325    0.071   18.683    0.000
##     calm              1.295    0.068   19.054    0.000
##     intentions        1.181    0.067   17.540    0.000
##   MR2 =~                                              
##     hungry            1.000                           
##     pain              1.020    0.032   31.985    0.000
##     tired             1.035    0.031   33.842    0.000
##     fear              1.024    0.031   33.022    0.000
##     pleasure          1.005    0.031   31.979    0.000
##     free_will         0.804    0.035   23.054    0.000
##     safe              0.921    0.032   28.355    0.000
##     conscious         0.881    0.036   24.521    0.000
##     desires           0.910    0.034   26.861    0.000
##   MR3 =~                                              
##     temperature       1.000                           
##     seeing            1.309    0.061   21.375    0.000
##     sounds            1.123    0.054   20.782    0.000
##     depth             1.097    0.060   18.223    0.000
##     remembering       1.135    0.058   19.663    0.000
##     goal              0.961    0.062   15.569    0.000
##     communicating     1.163    0.057   20.330    0.000
##     choices           1.179    0.059   19.934    0.000
##     odors             1.243    0.061   20.235    0.000
##     recognizing       1.180    0.059   19.987    0.000
##     computations      0.356    0.065    5.502    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   MR1 ~~                                              
##     MR2               2.968    0.259   11.462    0.000
##     MR3               1.897    0.182   10.448    0.000
##   MR2 ~~                                              
##     MR3               2.995    0.263   11.401    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     embarrassed       1.587    0.111   14.249    0.000
##     guilt             1.402    0.099   14.151    0.000
##     pride             1.243    0.090   13.882    0.000
##     beliefs           1.681    0.117   14.357    0.000
##     disrespected      1.598    0.112   14.232    0.000
##     love              1.183    0.087   13.613    0.000
##     depressed         1.536    0.110   13.949    0.000
##     emo_recog         1.347    0.095   14.132    0.000
##     morality          1.711    0.119   14.327    0.000
##     personality       1.049    0.078   13.381    0.000
##     joy               1.041    0.079   13.245    0.000
##     happy             1.135    0.085   13.406    0.000
##     self_restraint    1.686    0.118   14.284    0.000
##     thoughts          1.548    0.111   13.950    0.000
##     angry             1.519    0.110   13.799    0.000
##     reasoning         2.072    0.144   14.359    0.000
##     self_aware        1.874    0.132   14.247    0.000
##     nauseated         1.995    0.142   14.077    0.000
##     calm              1.730    0.123   14.015    0.000
##     intentions        2.095    0.147   14.224    0.000
##     hungry            1.186    0.090   13.230    0.000
##     pain              0.943    0.074   12.782    0.000
##     tired             0.730    0.060   12.149    0.000
##     fear              0.815    0.065   12.460    0.000
##     pleasure          0.918    0.072   12.783    0.000
##     free_will         1.844    0.131   14.081    0.000
##     safe              1.257    0.093   13.521    0.000
##     conscious         1.854    0.133   13.962    0.000
##     desires           1.480    0.108   13.721    0.000
##     temperature       1.458    0.107   13.598    0.000
##     seeing            1.386    0.109   12.723    0.000
##     sounds            1.186    0.091   13.001    0.000
##     depth             2.009    0.146   13.736    0.000
##     remembering       1.578    0.118   13.392    0.000
##     goal              2.617    0.185   14.125    0.000
##     communicating     1.422    0.108   13.176    0.000
##     choices           1.603    0.120   13.309    0.000
##     odors             1.659    0.126   13.210    0.000
##     recognizing       1.585    0.119   13.293    0.000
##     computations      4.180    0.286   14.632    0.000
##     MR1               2.254    0.240    9.400    0.000
##     MR2               5.114    0.423   12.083    0.000
##     MR3               2.529    0.256    9.878    0.000

## Warning in lav_data_full(data = data, group = group, group.label =
## group.label, : lavaan WARNING: unordered factor(s) with more than 2 levels
## detected in data: subid

## Warning in lav_partable_check(lavpartable, categorical = categorical, warn
## = TRUE): lavaan WARNING: parameter table does not contain thresholds

## Loading required package: proto

ModelWDM: Theoretical, three factors (AFFECT, AUTONOMY, PERCEPTION; see Weisman et al., 2015)

## lavaan (0.5-20) converged normally after  50 iterations
## 
##   Number of observations                           431
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              699.397
##   Degrees of freedom                               101
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             7057.942
##   Degrees of freedom                               120
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.914
##   Tucker-Lewis Index (TLI)                       0.898
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -12281.509
##   Loglikelihood unrestricted model (H1)     -11931.810
## 
##   Number of free parameters                         35
##   Akaike (AIC)                               24633.017
##   Bayesian (BIC)                             24775.331
##   Sample-size adjusted Bayesian (BIC)        24664.261
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.117
##   90 Percent Confidence Interval          0.109  0.126
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.057
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   affect =~                                           
##     happy             1.000                           
##     depressed         0.808    0.034   23.676    0.000
##     fear              0.943    0.034   27.927    0.000
##     angry             0.946    0.032   29.776    0.000
##     calm              0.913    0.031   29.827    0.000
##     joy               1.008    0.028   35.957    0.000
##   perception =~                                       
##     sounds            1.000                           
##     seeing            1.177    0.045   26.103    0.000
##     temperature       0.905    0.041   22.316    0.000
##     odors             1.114    0.046   24.067    0.000
##     depth             0.939    0.048   19.465    0.000
##   autonomy =~                                         
##     free_will         1.000                           
##     choices           1.023    0.046   22.189    0.000
##     self_restraint    0.758    0.044   17.403    0.000
##     intentions        1.028    0.047   21.949    0.000
##     goal              0.856    0.049   17.385    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   affect ~~                                           
##     perception        3.186    0.277   11.511    0.000
##     autonomy          3.677    0.309   11.906    0.000
##   perception ~~                                       
##     autonomy          2.902    0.254   11.409    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     happy             0.802    0.072   11.064    0.000
##     depressed         1.909    0.139   13.704    0.000
##     fear              1.655    0.126   13.141    0.000
##     angry             1.372    0.107   12.808    0.000
##     calm              1.273    0.099   12.797    0.000
##     joy               0.788    0.072   10.942    0.000
##     sounds            1.061    0.091   11.677    0.000
##     seeing            1.128    0.105   10.761    0.000
##     temperature       1.275    0.101   12.648    0.000
##     odors             1.455    0.122   11.971    0.000
##     depth             2.126    0.159   13.375    0.000
##     free_will         1.541    0.127   12.135    0.000
##     choices           1.348    0.116   11.625    0.000
##     self_restraint    1.810    0.135   13.449    0.000
##     intentions        1.431    0.122   11.778    0.000
##     goal              2.311    0.172   13.453    0.000
##     affect            5.084    0.400   12.708    0.000
##     perception        3.313    0.294   11.259    0.000
##     autonomy          3.605    0.342   10.540    0.000

## Warning in lav_data_full(data = data, group = group, group.label =
## group.label, : lavaan WARNING: unordered factor(s) with more than 2 levels
## detected in data: subid

## Warning in lav_partable_check(lavpartable, categorical = categorical, warn
## = TRUE): lavaan WARNING: parameter table does not contain thresholds

ModelGGW: Theoretical, two factors (AGENCY, EXPERIENCE; see Gray et al., 2007)

## lavaan (0.5-20) converged normally after  42 iterations
## 
##   Number of observations                           431
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             1653.966
##   Degrees of freedom                               134
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             8749.306
##   Degrees of freedom                               153
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.823
##   Tucker-Lewis Index (TLI)                       0.798
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -13782.271
##   Loglikelihood unrestricted model (H1)     -12955.288
## 
##   Number of free parameters                         37
##   Akaike (AIC)                               27638.543
##   Bayesian (BIC)                             27788.989
##   Sample-size adjusted Bayesian (BIC)        27671.572
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.162
##   90 Percent Confidence Interval          0.155  0.169
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.083
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   experience =~                                       
##     hungry            1.000                           
##     fear              1.047    0.044   23.972    0.000
##     pain              1.030    0.045   23.047    0.000
##     pleasure          1.098    0.041   26.543    0.000
##     angry             1.020    0.043   23.796    0.000
##     desires           1.013    0.042   24.228    0.000
##     personality       0.997    0.041   24.245    0.000
##     conscious         0.955    0.044   21.559    0.000
##     pride             0.771    0.041   18.909    0.000
##     embarrassed       0.595    0.040   14.786    0.000
##     joy               1.056    0.042   25.189    0.000
##   agency =~                                           
##     self_restraint    1.000                           
##     morality          0.913    0.055   16.657    0.000
##     remembering       1.099    0.062   17.798    0.000
##     emo_recog         0.996    0.054   18.371    0.000
##     goal              1.016    0.064   15.872    0.000
##     communicating     1.076    0.062   17.297    0.000
##     thoughts          1.227    0.063   19.419    0.000
## 
## Covariances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##   experience ~~                                       
##     agency            2.862    0.256   11.199    0.000
## 
## Variances:
##                    Estimate  Std.Err  Z-value  P(>|z|)
##     hungry            1.922    0.140   13.774    0.000
##     fear              1.381    0.104   13.296    0.000
##     pain              1.615    0.119   13.535    0.000
##     pleasure          0.807    0.067   12.065    0.000
##     angry             1.362    0.102   13.346    0.000
##     desires           1.223    0.093   13.217    0.000
##     personality       1.181    0.089   13.211    0.000
##     conscious         1.837    0.133   13.817    0.000
##     pride             1.904    0.135   14.137    0.000
##     embarrassed       2.291    0.159   14.411    0.000
##     joy               1.069    0.083   12.856    0.000
##     self_restraint    1.453    0.113   12.888    0.000
##     morality          1.672    0.125   13.387    0.000
##     remembering       1.896    0.146   13.022    0.000
##     emo_recog         1.366    0.107   12.790    0.000
##     goal              2.442    0.180   13.584    0.000
##     communicating     2.029    0.154   13.196    0.000
##     thoughts          1.612    0.132   12.242    0.000
##     experience        4.377    0.411   10.638    0.000
##     agency            2.430    0.251    9.675    0.000

## Warning in lav_data_full(data = data, group = group, group.label =
## group.label, : lavaan WARNING: unordered factor(s) with more than 2 levels
## detected in data: subid

## Warning in lav_partable_check(lavpartable, categorical = categorical, warn
## = TRUE): lavaan WARNING: parameter table does not contain thresholds

Compare models (if possible)

# compare models (iff continuous and ML)
customVuong(d4_all_fitDD, d4_all_fitWDM, d4_all_fitGGW)

## $mod1_v_mod2
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 79.858,   p = <2e-16
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -93.720,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -93.720,   p = < 2.2e-16
## 
## $mod1_v_mod3
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 66.793,   p = <2e-16
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -93.631,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -93.631,   p = < 2.2e-16
## 
## $mod3_v_mod2
## 
## Model 1 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## Model 2 
##  Class: lavaan 
##  Call: lavaan::lavaan(model = model, data = d, model.type = "cfa", int.ov.free = TRUE,  
## 
## 
## Variance test 
##   H0: Model 1 and Model 2 are indistinguishable 
##   H1: Model 1 and Model 2 are distinguishable 
##   w2 = 16.197,   p = <2e-16
## 
## Non-nested likelihood ratio test 
##   H0: Model fits are equal for the focal population 
##   H1A: Model 1 fits better than Model 2 
##   z = -17.962,   p = 1
##   H1B: Model 2 fits better than Model 1 
##   z = -17.962,   p = < 2.2e-16
## 
## $winner
## [1] "WDM"